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THE  LIBRARY 

OF 

THE  UNIVERSITY 

OF  CALIFORNIA 

LOS  ANGELES 


GIFT  OF 

U.  of  Calif. 
Berkeley 


The 

Design  of  Marine  Engines 

and  Auxiliaries 


BY 


EDWARD   M.   BRAGG,   S.  B. 

Professor  of  Naval  Architecture  and  Marine  Engineering 
University  of  Michigan 


110  ILLUSTBATIOXS 
and  folding  plates 


NEW  YORK 

D.   VAN    NOSTRAND    COMPANY 

25   Park   Place 

1916 


^'m(i 


Copyright,  1916, 

BY 

D.    VAN    NOSTRAND    COMPANY 


Stanbopc  iprcss 

F.    H.GILSON    COMPANY 
BOSTON,  U.S.A. 


Libran 

VAl 

PREFACE 


The  production  of  a  book  upon  marine  engine  design  must 
necessarily  involve  the  use  of  material  from  many  sources.  It 
is  so  difficult  to  determine  the  ultimate  source  of  all  this  material 
that  the  author  has  not  attempted  the  task.  It  is  far  easier  to 
point  out  those  portions  of  the  book  which  have  some  degree  of 
originality  and  then  to  make  a  general  acknowledgment  of  in- 
debtedness for  the  remainder. 

So  far  as  the  author  knows  the  following  methods  are  original: 
the  method  of  design  (§§  13  to  22),  the  method  of  obtaining  mean 
bearing  loads  (§§  86  to  90) ,  the  use  of  the  mean  lead  in  the  solu- 
tion of  valve  diagrams  (§  105),  the  method  of  designing  condensers 
(§  156),  the  method  of  designing  turning  engines  (§§  173  to  177). 

In  the  section  on  Engine  Balancing,  although  no  portion  of 
the  material  is  original,  much  time  and  effort  has  been  expended 
in  correlating  the  work  of  various  investigators. 

The  question  of  pressures  upon  main  bearings  will  be  found 
more  extensively  treated  in  a  paper  by  the  author  in  Vol.  18, 
Part  I,  of  The  Journal  of  the  American  Society  of  Naval 
Engineers. 

The  author  wishes  to  acknowledge  the  kindness  of  the  Newport 
News  Shipbuilding  and  Dry  Dock  Company  in  permitting  him 
to  use  certain  drawings  for  Plates  1,2,  and  3. 

E.  M.  BRAGG. 

Ann  Arbor,  Michigan. 
Sept.  15,  1916. 


737339 

Bnpineeting 
Library 


CONTENTS 


SECTION  I 

DETERMINATION   OF  CYLINDER  DIMENSIONS 

Par.\graph  Page 

1.  Conversion  of  Heat  into  Work i 

2.  Measurement  of  Power i 

3.  Mean  Referred  Pressure i 

4.  Design  Factors 2 

5.  Conditions  Affecting  Design  Factors 6 

6.  Superheated  Steam 7 

7.  Reheating 9 

8.  Jacketing 10 

9.  Effects  of  Cut-off II 

10.  Vacuum 13 

1 1 .  Crank  Arrangement 13 

12.  Mean  Effective  Pressure 14 

13.  Size  of  L.P.  Cylinder 19 

14.  Number  of  Expansions 19 

15.  Size  of  H.P.  Cylinder 20 

16.  Clearances 20 

17.  Cut-offs ,  21 

18.  Sizes  of  Intermediate  Cylinders 21 

19.  Stroke 22 

20.  Superheat  Factor 22 

21.  Distribution  of  Power 23 

22.  Example  of  Design 23 

23.  Steam  Consumption 28 

24.  Distribution  of  Work  at  Reduced  Powers 30 

25.  Variation  of  Revolutions  and  M.R.P.  at  Reduced  Power 33 

SECTION   II 
DESIGN   OF   ENGINE   PARTS 

26.  Effect  of  Character  of  Load 34 

27.  Working  Stress  Factors 34 

28.  Threaded  Parts 36 

29.  Column  Formula 37 

30.  Hollow  Columns 38 

31.  Bearing  Pressures 38 

32.  Types  of  Shafting 40 

V 


vi  CONTENTS 

Paragraph  Pack 

^^.   Equivalent  Twisting  or  Bending  Moments 41 

34.  Mean  Twisting  Moment 41 

35.  Maximum  Twisting  Moment 42 

36.  Maximum  Bending  Moment 43 

37.  Shaft  Diameter  from  Equivalent  Twisting  Moment 43 

38.  Shaft  Diameter  from  Equivalent  Bending  Moment 44 

39.  Coupling  Bolts 45 

40.  Sizes  of  Crank-shaft  Parts 46 

41.  Lloyd's  Rules  for  Determining  Sizes  of  Shafts  (1915-16) 46 

42.  Internal  Combustion  Engines 48 

43.  Masses  Affecting  Torsional  Vibration 49 

44.  Equivalent  Masses  at  Crank  Circle 49 

45.  Relation  between  Force  and  Amplitude  of  Vibration 50 

46.  Angle  of  Twist 5° 

47.  Equivalent  Shaft  Length  for  Reduced  Diameter 51 

48.  Crank-shaft  Mass  and  Propeller  Mass  . 51 

49.  Rate  of  Vibration 52 

50.  Load  upon  Piston  Rod 53 

51.  Diameter  of  Piston  Rod 53 

52.  Piston-rod  Ends 54 

53.  Types  of  Crosshead 55 

54.  Size  of  Crosshead  Pins 57 

55.  Size  of  Crosshead  Block 57 

56.  Types  of  Slippers 58 

57.  Size  of  Slipper 60 

58.  Thickness  of  Slipper 60 

59.  Backing  Guide 61 

.  60.   Backing-guide  Bolts 61 

61.  Attachment  of  SUpper 62 

62.  Types  of  Connecting  Rods 62 

63.  Diameter  of  Connecting  Rod 63 

64.  Taper  of  Body  of  Rod 65 

6j.    Connecting-rod  Bolts 66 

66.  Connecting-rod  Boxes 66 

67.  Connecting-rod  Fork 66 

68.  Coimecting-rod  Caps 68 

69.  Connecting-rod  Brasses 68 

70.  Tj'pes  of  Pistons 69 

71.  Cast-iron  Piston 69 

72.  Cast-steel  Pistons 70 

73.  Piston  Rings 71 

74.  Piston  Rims 72 

75.  Cj'hnder  Castings 72 

76.  Cylinder  Ends 72 

77.  Sizes  of  Parts 72 

78.  Attachment  of  Liner 74 

79.  Piston  Clearances 75 

80.  Ports  and  Passages 75 


CONTENTS  VU 

Paragraph  Page 

8i .  Cylinder  Openings 76 

82.  Cylinder  Feet 76 

83.  Boring-bar  Opening 77 

84.  Cylinder-cover  Studs 77 

85.  Valve-chest  Cover  and  Studs 78 

86.  Character  of  Loads  upon  Bearings 78 

87.  Loads  upon  Main  Bearings 80 

88.  Centrifugal  Force  of  Crank 82 

89.  Combined  Bearings 82 

90.  Crank-pin  Load 83 

91 .  Cylinder  Supports 83 

92.  Column  Flanges 84 

93.  Cylinder-column  Bolts 84 

94.  Engine  Beds 85 

95.  Main-bearing  Bolts 86 

96.  Main-bearing  Caps 87 

97.  Sequence  of  Cylinders 87 

98.  Space  Occupied  by  Engines 88 

99.  Eccentricity 89 

100.  Steam  Speeds 89 

loi.  Width  of  Ports 89 

102.  Steam  Lead 90 

103.  Size  of  Piston  Slide  Valve 90 

104.  Size  of  Flat  Slide  Valve 91 

105.  Valve  Diagram 91 

106.  Piston  Valves 93 

107.  Load  upon  Valve  Stems 94 

loS.  \'alve-stem  Bending 95 

109.  Drag  Rods 97 

no.  Yokes 97 

111.  Eccentric  Rods 97 

112.  Link  Bars 97 

113.  Link-block  Pin 98 

1 14".  Eccentrics 99 

115.  Eccentric  Strap 99 

116.  Reverse-shaft  Levers 100 

117.  Reverse  Shaft 100 

118.  Valve  Stem  Load 100 

SECTIOX   III 
ENGINE   BALANCING 

119.  Vertical  Forces  Balanced 102 

120.  Motion  of  Parts 102 

121.  Division  of  Connecting  Rod 102 

122.  Error  in  Division  of  Connecting  Rod 103 

123.  Balance  of  Rotating  Masses 105 

1 24.  Acceleration  of  Crosshead 107 


vm  CONTENTS 

Paragraph  Page 

125.  Primary  and  Secondary  Masses 109 

1 26.  Approximations no 

127.  Valve  Gear  Treated  as  Rotating  Mass no 

128.  Balance  with  Bob  Weights in 

129.  Balance  without  Use  of  Extra  Weights in 

130.  Equations  for  Force  and  Moment  Diagrams 112 

131.  Order  in  which  Equations  Must  be  Used 114 

132.  Number  of  Unknown  Quantities 115 

133.  Single-crank  Engine 115 

134.  Two-crank  Engine 115 

135.  Three-crank  Engine 116 

136.  Four-crank  Engine 117 

137.  Yarrow-Schlick-Tweedy  System 117 

138.  Unsymmetrical  Four-crank  Arrangement 119 

139.  Engines  with  Five  or  Six  Cranks 122 

140.  Summary 124 

SECTION   IV 
CONDENSERS  AND   AIR  PUMPS 

141.  Partial  Pressures 125 

142.  Effect  of  Air  upon  Rate  of  Condensation 125 

143.  Tube  Length 129 

144.  Rate  of  Heat  Transmission 129 

145.  Velocity  of  Cooling  Water 130 

146.  Jet  Condensers 131 

147.  Surface  Condensers 131 

148.  EfiScienc)'  of  Cooling  Surface 132 

149.  Comparison  of  Old  and  New  Types  of  Condensers 135 

1 50.  High  Vacua 136 

151.  Means  Employed  to  Obtain  High  Vacua 136 

152.  Augmentor  Condenser 138 

153.  Two-stage  Air  Pumps 138 

154.  Neilson's  Formula  for  Condenser  Design 139 

155.  Weighton's  Experiments 140 

156.  A  Method  of  Design  Based  upon  Weighton's  Experiments 142 

157.  Velocity  of  Cooling  Water 145 

158.  Effect  of  Surface-section  Ratio 147 

159.  Effect  of  Admitting  Water  at  Top  and  Bottom  of  Condenser 148 

160.  Admission  of  Steam  to  Condenser 148 

161.  Sizes  of  Condenser  Tubes 149 

162.  Relation  of  Air  Pump  and  Condenser 149 

163.  Neilson's  Diagram 15° 

164.  McBride's  Diagram 150 

165.  Determ.ination  of  Air  Leakage 153 

166.  Air  Leakage  Allowed  for  by  Manufacturers 153 

167.  Air  Leakage  in  Delaware's  Engines 154 

168.  Air-pump  Capacity i55 


CONTENTS  IX 

Paragraph  Page 

169.  Attached  Air  Pumps 156 

170.  Air  Pump  Proportions 157 

171.  Tj^pcs  of  Air  Pumps 159 

172.  Condition  for  Maximum  Load 164 

SECTION   V 
TURNING  ENGINES  AND   REVERSING  ENGINES 

173.  Type  of  Engine 167 

174.  Frictional  Load 167 

1 75.  Power  of  Turning  Engine 168 

176.  Proportions  of  Teeth  of  Worm  and  WTieel 169 

177.  Design  of  Worm  and  Wheel 169 

178.  Types  of  Reversing  Engines 17.5 

179.  Direct-acting  Engine 1 74 

180.  All-round  Gear 175 

181.  Cushioning  Dexices 176 

182.  Floating-lever  Gear 178 

183.  Brown  Gear 178 


The  Design  of  Marine  Engines 
and  Auxiliaries 


SECTION  I 
DETERMINATION  OF  CYLINDER  DIMENSIONS 

1.  Conversion  of  Heat  into  Work.  —  The  object  of  any  heat 
engine  is  to  convert  heat  into  work  and  the  working  fluid  is  taken 
into  the  engine  at  a  certain  temperature  and  rejected  at  a  lower 
temperature.  The  conversion  of  heat  into  work  in  the  case  of  a 
steam  engine  is  accompanied  by  a  reduction  of  temperature  and 
pressure  of  the  working  fluid,  and  by  an  increase  in  its  volume. 
This  reduction  of  temperature  may  be  accomplished  in  one 
cylinder  or  in  many  cylinders.  If  the  reduction  takes  place  in 
one  cylinder  the  engine  is  called  a  simple  engine,  or  single-stage 
expansion  engine;  if  the  temperature  is  reduced  in  two  stages 
the  engine  is  called  a  Compound,  or  two-stage  expansion  engine; 
if  in  three  stages  a  Triple,  or  three-stage  expansion  engine;  if  in 
four  stages  a  Quadruple,  or  four-stage  expansion  engine. 

2.  Measurement  of  Power.  —  The  power  developed  by  a 
heat  engine  can  be  measured  by  the  change  in  temperature  of  the 
working  fluid  and  also  by  the  change  in  pressure  and  volume. 
In  the  case  of  reciprocating  engines  it  is  more  convenient  to 
measure  the  power  in  the  latter  way  and  the  steam  indicator  is 
used  for  this  purpose.  In  designing  engines  it  is  usual  to  as- 
sume some  theoretical  relation  between  the  pressure  and  volume 
of  the  working  fluid  and  then  allow  for  the  variation  of  the 
actual  from  the  assumed  relation  by  means  of  a  design  factor. 

3.  Mean  Referred  Pressure.  —  The  actual  performance  of 
the  engine  is  determined  by  means  of  indicator  cards,  and  for 
design  purposes  it  is  usual  to  reduce  the  m.e.p.'s  of  cards  ob- 


2  THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

tained  from  different  cylinders  to  an  equivalent  m.e.p.  when 
spread  over  the  area  of  the  low-pressure  cylinder.  The  sum  of 
the  equivalent  m.e.p.  's  for  all  the  cylinders  of  an  engine  is  called 
the  mean  referred  pressure. 

HP  area 

m.e.p.//-— ■   =  m.T.p.H, 

LP  area 

MP  area 

m.e.p.j/  Y^ =  m.r.p..v, 

LP  area 

m.e.p.i^  =  m.r.p./, 
M.R.P. 

The  ratio  of  this  M.R.P.  to  the  theoretical  M.E.P.  obtained 
from  the  assumed  relation  of  pressure  and  volume  is  called  the 
design  factor. 

M.R.P. 

M.E.P. " 

4.  Design  Factors.  — ■  It  is  usual  to  calculate  the  theoretical 
mean  effective  pressure  by  means  of  a  formula  involving  the 
initial  pressure  (absolute)  of  the  steam,  the  number  of  expan- 
sions, the  pressure-volume  ratio,  and  the  absolute  back  pressure. 
The  theoretical  m.e.p.  will  vary,  depending  upon  what  values 
are  used  for  these  various  quantities.  In  some  systems  of  data 
keeping  the  initial  pressure  Pi  is  taken  as  the  boiler  pressure, 
in  others  as  boiler  pressure  minus  five  pounds,  and  in  others  as 
the  maximum  pressure  in  the  high-pressure  cylinder.  The  back 
pressure  Pb  is  sometimes  taken  as  zero,  in  other  cases  as  four 
pounds  absolute,  and  in  other  cases  as  the  actual  mean  back 
pressure  in  the  low-pressure  cylinder.  The  pressure-volume 
ratio  is  usually  taken  for  convenience  as  p. v.  =  constant,  al- 
though in  some  cases  it  is  taken  as  p.v.^s  =  constant.  The 
number  of  expansions  R  used  may  be  the  nominal  number, 
taldng  no  account  of  clearance  and  piston  rods,  or  it  may  be 
the  actual  number  Ra,  in  which  case  clearances  and  piston  rods 
are  included.  Sometimes  the  pressure-volume  curve  is  drawn 
tangent  to  the  point  of  cut-off  of  the  high-pressure  indicator 
card.     (See  Fig.  i.) 


DETERMINATION  OF   CYLINDER  DIMENSIONS 


If  the  pressure-volume  ratio  is  assumed  to  be  p. v.  =  constant 
the  following  result  will  be  obtained: 


M.E.P.  =P,^^t|>SL^_p^. 


The  design  factor  will  be 


M.R.P. 


p^l±}2E^_p^ 


R 


It  follows  from  (2)  that 

M.R.P.  =[^P,lilMi^-i>,]F. 


(i) 
(2) 

(3) 


Fig.  I. 

The  above  expression  gives  good  results  when  dealing  with 
engines  having  about  the  same  Pb,  but  now  that  engines  are  often 
used  in  combination  with  a  low-pressure  turbine  the  back  pressure 
may  be  10  pounds  absolute,  or  even  higher,  and  more  consistent 
results  will  be  obtained  with  the  following  expression: 

M.R.P.  +  Pb 


F  = 


p     I    -f    lOgeRg' 


R. 


M.R.P.     =    p.  I    +    log.  i?ap    _    p^ 


(4) 


(5) 


THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


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DETERMINATION  OF   CYLINDER   DIMENSIONS  5 

The  quantity  M.R.P.  +  Pb  will  be  designated  as  M.R.Pq- 
In  Fig.  3  will  be  found  values  of  F  plotted  upon  R^  as  abscissae. 
These  values  of  F  were  obtained  by  taking  for  Pi  the  maximum 
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A  study  of  these  factors  will  show  that  they  are  not  by  any 
means  constant.  They  vary  with  the  number  of  expansions 
and  also  with  the  initial  steam  pressure.  There  is  nothing  in 
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for  a  given  number  of  expansions.  In  fact,  if  the  above  equa- 
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Pi  I+l0gei?„' 

it  can  be  seen  that  an  equation  of  the  form, 

M.R.P.  -\-  Pb 


G  = 


Pi 


would  be  just  as  constant  for  any  given  value  of  R^  as  is  Formula 

(4) .     The  term  — ^ — — -  merely  serves  to  make  the  values  of 

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F  vary  less  in  going  from  one  value  of  Ra  to  another. 

For  this  reason  the  following  expression  has  been  used  to 

obtain  a  design  factor  H: 

Values  of  F  and  H  for  several  engines  are  given  in  Figs.  2  and 
3,  and  portions  of  these  figures  are  plotted  to  a  larger  scale  in 
Figs.  4  and  5.  It  will  be  noticed  that  while  the  values  of  H 
vary  more  with  Ra  than  do  the  values  of  F,  yet  for  any  given 
value  of  Ra  the  values  of  H  are  more  constant. 

A  mean  Hne  drawn  through  the  values  of  H  will  enable  us  to 
work  back  and  get  values  of  F  for  different  initial  pressures  as 


6  THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


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shown  in  Fig.  6.     The  curves  in  this  figure  give  the  relation 

p 
between  F,  M.R.P.o  and— ^-     It  will  be  noticed  that  the  values 

of  F  decrease  as  P,  increases,  and  that  for  any  given  value  of 
Pi  there  seems  to  be  a  minimum  value  of  F  when  Ra  =  9. 

5.   Conditions  Affecting  Design  Factors.  —  Before  proceeding 
to  make  use  of  F  and  //  for  design  purposes  it  will  be  necessary 


DETERMINATION  OF   CYLINDER   DIMENSIONS  7 

to  know  how  these  factors  are  affected  by  the  various  conditions 
that  may  exist  in  an  engine.  Our  expressions  for  F  and  H  con- 
tain only  functions  of  M.R.P.o,  Pi,  and  Ra,  whereas  such  con- 
ditions as  the  amount  of  superheat,  reheating,  jacketing,  cut-offs 
used,  wetness  of  steam,  valve  leakage,  etc.,  all  have  their  effects. 


and  our  expressions  should  contain  functions  of  all  these  if  we 
wish  to  get  constant  values. 

In  the  problem  of  engine  design  we  must  keep  clearly  in  mind 
the  difference  between  those  conditions  which  make  for  maximum 
power  and  those  which  make  for  maximum  economy.  The  two 
sets  of  conditions  are  not  identical  and  most  engines  are  a  com- 
promise between  these  conditions. 

6.  Superheated  Steam.  —  The  use  of  superheated  steam 
affects  the  engine  in  three  ways:  it  decreases  pounds  of  steam  per 
i.h.p.;  it  decreases  the  mean  referred  pressure,  and  so  decreases 
the  design  factor;  and  it  decreases  the  mechanical  efficiency  of 
the  engine. 

When  the  steam  enters  the  cylinder  it  gives  up  a  certain 
amount  of  heat  to  the  walls.  If  the  steam  is  saturated  this 
giving  up  of  heat  will  be  accompanied  by  a  precipitation  of  water 


8 


THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


upon  the  cylinder  walls,  and  due  to  the  presence  of  this  water 
the  interchange  of  heat  between  steam  and  walls  will  be  greatly 
accelerated.  If  superheated  steam  is  used  it  can  lose  some  heat 
without  causing  precipitation  and  the  loss  of  heat  to  the  cylinder 
walls  will  be  greatly  reduced.  This  condensation  of  steam, 
while  detrimental  to  economy,  is  beneficial  to  the  mechanical 
efficiency  since  the  water  acts  as  a  lubricant.  For  this  reason 
the  steam  consumption  should  always  be  referred  to  the  brake 
horse-power. 

Superheating  the  steam  makes  it  less  dense  and  gives  leaner 
indicator  cards;  hence  an  engine  must  be  larger  for  a  given  power 

1.00 
.99 


.89 


.87 


o  ^«^   *   s 


0  10  20  30  40  50  60  70  80  90  100  110  120  130  140  150  160 
Superheat,  °F. 

Fig.  7. 

than  when  saturated  steam  is  used.  Fig.  7  shows  the  effect  of 
superheat  upon  the  design  factor  as  deduced  from  the  trials  of 
the  steam-yacht  Idalia.  In  Fig.  4  it  will  be  noticed  that  certain 
points  marked  S,  indicating  that  superheated  steam  was  used, 
are  below  the  points  for  engines  using  saturated  steam. 

It  is  usually  estimated  that  there  is  i  per  cent  decrease  in  the 
pounds  of  steam  used  per  i.h.p.  for  every  10°  F.  superheat,  for 
moderate  ranges  of  superheat.  In  marine  practice  it  is  generally 
considered  best  not  to  use  more  than  175°  or  200°  F.  superheat 


DETERMINATION   OF   CYLINDER   DIMENSIONS  9 

at  the  engine  as  troubles  are  experienced  when  the  temperature 
of  the  steam  exceeds  600°  F. 

Since  with  superheated  steam  we  get  leaner  indicator  cards 
and  since  the  superheat  decreases  as  we  go  towards  the  L.P. 
cylinder,  the  distribution  of  power  will  be  different  in  an  engine 
when  using  superheated  steam  from  what  it  is  when  using  satu- 
rated steam.  The  effect  of  superheat  is  to  cause  the  L.P. 
cylinder  to  do  a  larger  percentage  of  the  total  work. 

In  this  connection  it  is  interesting  to  note  that  the  values  of 
F  and  H  for  the  U.S.S.  Michigan,  using  steam  superheated  about 
88°,  fall  below  the  average  of  those  using  saturated  steam,  as 
would  be  expected.  In  the  case  of  the  U.S.S.  Delaware,  how- 
ever, the  values  are  above  the  average,  and  in  the  case  of  the 
Creole  are  just  about  the  same  as  those  for  saturated  steam. 
The  reason  for  this  will  be  explained  later. 

7.  Reheating.  —  Reheating  the  steam  between  cylinders  has 
the  effect  of  increasing  the  design  factor  as  is  shown  in  the  case 
of  the  pumping  engines  in  Fig.  2  which  are  marked  P.  It  will 
also  cause  the  steam  to  be  drier  in  the  M.P.  and  L.P.  cylinders 
and  by  decreasing  the  lubrication  will  cause  the  mechanical 
efficiency  to  be  lowered.  If  steam  from  the  boiler  is  used  as  a 
reheating  agent  the  total  pounds  of  steam  per  b.h.p.  may  in 
some  cases  be  increased.  As  in  the  case  of  superheated  steam 
the  steam  consumption  should  be  expressed  in  terms  of  the 
brake  horse-power.  Professor  Weighton  drew  the  following 
conclusions  from  experiments  made  upon  a  compound  engine 
(Inst,  of  Mech.  Eng.,  July,  1902). 

"  (i)  The  amount  of  steam  condensed  in  the  coils  is  inde- 
pendent of    the    temperature   difference    between    heating  and 
heated  steam  but  depends  upon  the  amount  of  heated  steam  used. 
"  (2)  The  influence  of  the  reheater  is  beneficial  in  the  following 
respects : 

{a)  Reduces  the  amount  of  condensation  in  receiver. 

{h)  Raises  receiver  pressure. 

(c)  Raises  mean  referred  pressure. 

{d)  Increases  the  r.p.m. 

{e)  Increases  the  dryness  of  steam  in  L.P.  cyhnder. 


lO        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


"  Detrimental  to  economy  in  the  following: 

(a)  Lowers  the  mechanical  efificiency  of  engine. 

(b)  Increases  the  steam  per  horse-power  developed." 

Reheating  also  affects  the  distribution  of  power.  It  increases 
the  receiver  pressures  and  so  increases  the  back  pressures  in  the 
H.P.  and  M.P.  cylinders.  This  throws  more  work  into  the  L.P. 
cylinder. 

It  is  generally  considered  in  the  United  States  that  reheating 
increases  the  economy  of  pumping  engines. 

8.  Jacketing.  —  The  effect  of  jacketing  upon  the  design  of 
the  engine  will  depend  upon  the  type  of  engine  and  the  extent 
of  jacketing.  The  following  results  are  taken  from  experiments 
made  by  Professor  Mellanby  upon  a  compound  engine  with 
cylinders  ii^"  and  20"  in  diameter  and  a  stroke  of  36". 


Pi  =155  pounds  (absolute), 
Pb  =  2.8  pounds  (absolute), 
R.P.M.  =  60, 


H.P.  L.P. 

Cut-off  =  0.25  0.52 
Clearance  —  0.092  0.07 
P.S.  =  360  feet  per  min. 


No  jackets 

H.P.  ends  jacketed 

H.P.  ends  and  barrel  jacketed.  . 
H.P.  ends,  barrel,  and  L.P.  ends 
H.P.  and  L.P.  ends  and  barrels. 
L.P.  ends  and  barrel 


Lbs.  o{|M.R.P.   M.R.F. 
steam    in  H.P.  in    L.P. 

per      ]     cyl..         cyL, 
I.H.P.       lbs.  lbs. 


18.2 

17.8 

17-4 

17 

17-3 

175 


21.8 


20.9 


143 
13.6 

134 

17 

19 


1  Per cent 
M.R.P.oiM.R.P.f, 
in  H.P. 


55-7 

57-2 

57.6 

49 

47 


0.75 
0.74 
0.74 
0.77 
0.81 


It  will  be  noticed  that  the  extent  of  the  jacketing  affected  the 
design  factor,  the  steam  consumption,  and  the  distribution  of 
power.  The  following  conclusions  are  drawn  from  experience 
and  the  results  of  experiments: 

"  All  causes,  superheat,  late  cut-offs,  working  noncondensing, 
high  speed  (short  stroke),  which  tend  to  raise  the  temperature 
of  the  walls  diminish  the  useful  effect  of  jackets.  Jackets 
afford  a  larger  surface  for  radiation.  Jackets  are  good  for 
engines  of  intermittent  action.  Saturated  steam  is  the  best 
medium  for  jacketing.     The  rates  of  heat  transmission  when 


7"- 

i:)2 

-  23" 

i8" 

7"- 

-  io|"  - 

-  23" 

DETERMINATION    OF    CYLINDER    DIMENSIONS  II 

walls  are  wet  and  when  dry  are  as  360  to  i.  Jackets  are  useful 
for  slow  revolution  but  not  for  quick  revolution  engines.  Jackets 
are  useful  for  compound  and  simple  engines  but  are  of  doubtful 
value  on  Triples  and  Quadruples." 

9.  Efifects  of  Cut-off.  —  The  cut-off  in  the  M.P.  and  L.P. 
cylinders  will  affect  the  total  power  developed,  as  shown  by  the 
experiments  of  Prof.  R.  L.  Weighton  upon  a  triple  expansion 
engine: 

Cut-offs 

0.67    —  0.67  —  0.67 

0-67    -  0.3335    -  0-67 

0.67    —  0.64    —  0.67 
18"  0.67    -  0.64    -  0.335 

0.67    —  0.64    —   0.25 

These  experiments  were  carried  out  by  Professor  Weighton 
primarily  to  investigate  the  effect  of  varying  cut-off  upon 
economy  and  as  a  result  of  the  experiments  the  following  con- 
clusions are  given : 

(See  ''Receiver  Drop  in  Multiple-expansion  Engines,"  North- 
East  Coast  Institute  of  Engineers  and  Shipbuilders,  Vol.  16.) 

"(i)  For  maximum  economy  of  consumption  steam  must  be 
cut  off  at  a  certain  point  of  the  stroke  in  the  larger  cylinders 
(LP.  and  L.P.)  of  multiple-expansion  engines.  For  any  given 
cylinder  this  point  depends  solely  upon  the  ratio  between  the 
capacities  of  that  cylinder  and  the  preceding  cylinder  (R),  and 
is  expressed  as  follows: 

Maximum-economy  cut-off  _  i 

Stroke  ~  °''^       r' 


*. 

M.R.P. 

201 

28.2 

201.5 

28.4 

201 

27.1 

202 

28.6 

200 

27.=; 

This  is  the  principal  and  most  important  conclusion  deduced 
from  the  trials. 

"(2)  It  follows  from  No.  i  that  the  cut-off  in  the  larger 
cylinders,  once  fixed,  should  never  be  altered,  whatever  may  be 
the  cut-off  in  the  high-pressure  cylinder,  or  the  steam  pressure 
employed.  This  means  that  automatic-expansion  governors, 
or  linking-up  gear,  should  act  upon  the  high-pressure  cylinder 
only,  if  maximum  economy  at  all  powers  is  to  be  preserved. 


12        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

"  (3)  The  cut-off  in  the  larger  cylinders  affects  materially  the 
total  horse-power  developed  by  the  engines.  As  regards  the 
low-pressure  cylinder  of  triples,  and  the  second  intermediate 
and  low-pressure  cylinders  of  quadruples,  maximum  power 
cut-off  in  these  cylinders  coincides  with  the  cut-off  of  maximum 
economy.  As  regards  the  second  cylinder  of  triples  and  quad- 
ruples, maximum  power  cut-off  is  very  considerably  later  than 
that  of  maximum  economy.  In  compounds  the  maximum 
power  cut-off  in  the  low-pressure  cylinder  is  only  sHghtly  later 
than  that  of  maximum  economy. 

"  (4)  When  cyHnder  ratio  (R)  is  small  —  say  from  2  to  2.5  — 
the  cut-off  in  the  larger  cylinders  may  be  varied  considerably 
from  that  corresponding  to  maximum  economy  without  any 
appreciable  fall  in  economy.  But  when  (R)  is  large  there  is  no 
such  permissible  deviation  without  entailing  as  a  consequence  a 
fall  in  efficiency. 

"(5)  With  given  efficiency  in  receiver  drop,  smallness  of 
cyHnder  ratio  is  conducive  to  smoothness  of  working,  uniformity 
of  turning,  durabihty,  handiness  in  starting  and  reversing,  and 
compactness  of  design." 

(In  getting  values  of  (R)  include  the  effect  of  piston  rods  and 
clearance  spaces.) 

The  above  conclusions  can  be  put  somewhat  more  concisely 
as  follows: 

For  economy  the  cut-off's  should  be  0.15  +-j,-     (Weigh ton.) 

R 

For  maximum  power  the  cut-off  should  be  (0.15  -)-  —  j  1.4  in 

LP.  cylinder. 

For  maximum  power  the  cut-off  should  be  (15  -f  -^j  in  L.P. 

cylinder. 

For  smooth  running  cut-offs  should  be  late. 

For  any  desired  distribution  of  power  the  cut-offs  should  be 
determined  from  the  curves  of  Fig.  12.  The  service  to  which 
the  engine  is  to  be  put  will  determine  which  of  these  conditions 
should  be  considered  the  most  important. 


DETERMINATION   OF   CYLINDER   DIMENSIONS  1 3 

In  connection  with  the  tests  carried  out  by  Professor  Weighton 
it  was  shown  that  the  mean  referred  pressure  obtained  from  an 
engine  varied  considerably,  dependent  ujion  the  cut-offs  used  in 
the  M.P.  and  L.P.  cylinders.  In  the  case  given  above  there  is 
a  variation  of  6  per  cent  due  to  this  cause  alone.  In  the  case 
of  the  U.S.S.  Deknvare  which  used  superheated  steam,  and  whose 
values  of  F  and  H  would  naturally  fall  below  those  for  saturated 
steam,  the  cylinder  proportions  and  cut-offs  appear  to  have 
been  so  favorable  that  the  increase  due  to  these  latter  conditions 
was  more  than  the  decrease  due  to  the  use  of  superheated 
steam. 

10.  Vacuum.  —  The  effect  of  vacuum  upon  economy  was  in- 
vestigated in  certain  experiments  carried  out  by  Professor 
Weighton.  He  found  that  the  number  of  pounds  of  steam  per 
brake  horse-power  was  least  at  a  vacuum  of  26  to  28  inches,  but 
that  the  number  of  heat-units,  working  from  H.P.  steam  chest 
to  hotwell,  per  brake  horse-power  was  least  at  20  inches  vacuum. 
While  the  horse-power  of  the  engine  is  increased  by  increasing 
the  vacuum,  it  causes  the  temperature  of  the  hotwell  to  be  lower 
and  it  is  possible  to  carry  the  cooKng  to  such  a  point  that  the 
coal  per  brake  horse-power  is  increased. 

Another  point  brought  out  by  these  experiments  was  that  in 
going  from  26  inches  vacuum  to  28  inches  vacuum  the  M.R.P. 
was  not  increased  by  the  equivalent  of  2  inches  of  mercury  but 
by  something  less  than  2  inches. 

It  was  also  shown  that  the  effect  of  increased  vacuum  was  not 
confined  entirely  to  the  L.P.  cylinder  but  reached  back  into  the 
M.P.  and  H.P.  cylinders  with  the  result  that  the  steam  con- 
sumption instead  of  remaining  constant  per  revolution  in- 
creased as  the  vacuum  increased.  Both  of  these  results  are 
probably  due  to  the  increased  range  of  temperature  in  the 
cylinders,  causing  an  increase  in  the  initial  condensation.  This 
effect  would  probably  be  greater  with  less  stages  of  expansion 
and  less  with  a  greater  number  of  stages. 

11.  Crank  Arrangement.  —  Experiments  were  carried  out  by 
Professor  Mellanby  to  ascertain  the  effect  of  crank  arrangement 
in  a  Quadruple  upon  steam  consumption.     It  was  found  that 


14        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

with  the  first  two  and  last  two  cranks  at  i8o°  the  engine  was 
more  economical  by  about  3  per  cent  than  when  the  cranks  were 
at  90°.  This  is  probably  due  to  the  fact  that  the  180°  arrange- 
ment gives  a  card  as  shown  by  Fig.  9,  while  the  90°  arrangement 
gives  a  card  like  Fig.  8.  In  the  latter  the  lowest  temperature 
occurs  at  the  end  of  the  stroke  when  the  piston  is  barely  moving 
and  the  full  area  of  the  walls  is  subjected  to  the  low  temperature 


Triple-Low  Leading 
Quacl.-90° 


Fig.  8.  .  Fig.  9. 

for  an  appreciable  time.  In  the  case  of  the  card  shown  in  Fig.  9, 
the  lowest  temperature  occurs  near  midstroke  when  the  piston, 
is  moving  fastest  and  only  about  half  of  the  area  of  the  walls  is 
subjected  to  the  low  temperature. 

In  triple-expansion  engines  the  "high-leading"  arrangement 
of  cranks  gives  an  indicator  card  similar  to  that  of  the  Quadruple 
with  cranks  at  180°,  while  the  "low-leading"  arrangement  gives 
a  card  similar  to  that  of  the  Quadruple  with  the  90°  arrangement. 

12.  Mean  Effective  Pressure.  —  The  mean  effective  pressure 
employed  for  the  production  of  power  under  any  given  set  of 
conditions  affects  the  economy  of  the  engine  very  materially. 

In  a  paper  read  before  the  Institute  of  Engineers  and  Ship- 
builders, in  Scotland,  and  printed  in  Vol.  50,  1906-7,  Mr.  R. 
Royds  made  certain  statements  concerning  the  best  mean 
effective  pressure  for  any  given  condition,  and  these  statements 
have  been  concurred  in  by  most  of  the  men  who  have  had  experi- 
ence in  testing  engines.     These  statements  are  as  follows : 

"(i)  The  higher  the  mean  effective  pressure,  the  lower  will 
be  the  first  cost  of  a  steam  engine  for  any  given  power. 

"(2)  For  multiple-expansion  unjacketed  condensing  engines, 
using  saturated  steam  at  about  165  pounds  per  square  inch 
absolute  in  the  engine  cylinder,  the  best  mean  effective  pressure 


DETERMINATION   OF    CYLINDER    DIMENSIONS  1 5 

for  normal  load  is  from  40  to  45  pounds  per  square  inch,  referred 
to  the  L.P.  cylinder,  and  the  economy  varies  but  slightly  for  a 
considerable  range  in  the  mean  effective  pressure. 

"  (3)  For  jacketed  multiple-expansion  condensing  engines, 
with  steam  pressure  as  above,  the  best  mean  effective  pressure 
is  slightly  lower  than  for  unjacketed  multiple-expansion  con- 
densing engines. 

"  (4)  Non-condensing  engines  have  a  best  mean  effective 
pressure  rather  higher,  and  the  variation  in  economy  for  any 
given  range  of  mean  effective  pressure  is  less  than  for  condensing 
engines. 

"(5)  For  steam  pressures  higher  than  165  pounds  per  square 
inch  absolute,  the  best  mean  effective  pressure  is  higher  than 
from  40  to  45  pounds  per  square  inch,  and  is  probably  as  high 
as  from  45  to  50  pounds  per  square  inch  referred  to  the 
L.P.  cylinder,  for  triple  or  quadruple-expansion  engines  using 
saturated  steam  over  200  pounds  per  square  inch  boiler 
pressure. 

"(6)  Multiple-expansion  engines  using  saturated  steam  below 
165  pounds  per  square  inch  absolute  have  their  best  mean 
effective  pressure  below  from  40  to  45  pounds  per  square  inch, 
and  this  best  mean  effective  pressure  falls  more  rapidly  with 
fall  of  steam  pressure  for  the  condensing  than  for  the  non- 
condensing  engine. 

"(7)  The  more  economical  an  engine  can  be  made,  the  lower 
is  likely  to  be  the  best  mean  effective  pressure,  though  not  to 
any  large  extent.  Hence,  large  engines  may  have  a  rather 
lower  best  mean  effective  pressure  than  small  engines  using 
steam  at  the  same  pressure. 

"  (8)  Engines  using  highly  superheated  steam,  so  that  the 
steam  is  superheated  during  expansion,  have  a  best  mean  eft'ective 
pressure  lower  than  for  engines  using  saturated  steam,  with  a 
consequent  increase  in  first  cost  for  any  given  power.  Such 
engines  have  a  high  thermal  efficiency,  and  will  maintain  the 
same  efficiency  over  a  wide  range  of  power. 

"(9)  The  best  mean  effective  pressure  is  about  35  pounds 
per   square    inch    for    single-cylinder    condensing    non-jacketed 


1 6        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

engines,  using  saturated  steam  at  about  75  pounds  per  square 
inch  absolute.  For  other  conditions  the  same  general  laws 
hold  good  as  for  multiple-expansion  engines." 

The  following  table  shows  somewhat  more  concisely  the  de- 
sirable mean  referred  pressure  for  different  conditions: 

TABLE    1 


Un jacketed,  non-condensing. 

"  condensing  .  .  .  . 

Jacketed,  condensing 

Superheated  slightly 

"  highly 


Single- 
cylinder, 
75  pounds 
absolute 


37 
35 
33 
32 
30 


Multiple- 
expansion, 
165  pounds 

absolute 


42-47 
40-45 
38-43 
36-41 
33-38 


Multiple- 
expansion, 
200  pounds 
absolute 


48-53 
45-50 
42-47 

40-45 
37-42 


Multiple- 
expansion, 
250  pounds 

absolute 


53-58 
50-55 
47-52 
45-50 
42-47 


The  steam  consumption  tests  carried  out  upon  H.M.S.  Ar- 
gonaut, U.S.S.  Birmingham,  U.S.S.  Delaware,  and  U.S.S.  Texas 
agree  with  these  conclusions.  Below  are  given  the  proportions 
of  the  engines  for  these  ships  and  some  of  the  results  of  the  tests 
for  steam  consumption. 

TABLE    2 


Diam.  of 
cylinder 

Per  cent 

Cylinder 

Cut-off  for 
maximum 
economy 

Jackets 

ance     1     ratio 

Liners 

Ends 

Argonaut  H 

(2)  L. ■■.;■.■. 

Birmingham  H  .. . 
I... 

{2)L... 

Delaware  H 

/ 

(2)L 

Texas  H 

^4, 
555 
64 

28i 

45 
62 

38^ 

57 

76 

39 
63 
83 

25 
20 

15 

26.2 

21.3 
21.  I 

16.2 

13-4 
12.4 

TA    2 

I 
2.6 

6.65 

h 

I 

2-IS 
7.6 

•54 

■54 

•55 
•  41 

.62 
•43 

•53 
■435 

yes 
yes 
3'es 

no 
no 
no 

yes 
yes 
yes 

no 

yes 

yes 

no 
no 
no 

no 
no 
no 

no 

yes 

yes 

no 

I 

(2)  L 

14           ,        2 . 64 

TC             \         n     '7-7 

yes 
yes 

.-, 

DETERMINATION  OF   CYLINDER  DIMENSIONS 


17 


TABLE  3 


I.H.P. 

R.P.M. 

Cut- 

oflFs 

H-I-L 

Actual 
expan- 
sions 

P. 
(abs.) 

M.R.P. 

Vac- 
uum, 
inches 

Su- 
per- 
heat 
at  en- 
gine 

Steam 
con- 
sump- 
tion, 
lbs. 

Max.  Power 

Argonaut 

Birmingham .  . . 

Delaware 

Te.\as 

Medium  Power 

Argonaut 

Birmingham .  . . 

Delaware 

Texas 

Low  Power 

Argonaut 

Birmingham .  . . 

Delaware 

Texas 

9.390 
7.385 
14.716 
14.213 

6,906 
5.431 

8.784 
9.489 

1.933 
1,565 
2,049 
2.339 

127.5 
192.2 
128.2 

124.4 

116. 3 
173.3 
108.8 
no. 3 

76.3 
113  2 
68 
69.2 

71-67-46 
79-75-60 
8&-80-62 
77-78-62 

73-67-46 
79-75-60 
86-70-38 
61-67-62 

73-67-46 
79-75-60 
86-70-38 
54-63-54 

8.7 
11.35 

8.7 
II. 6 

8.5 
n.35 

8.7 
14. 1 

8.5 
11-35 

8.7 
IS. 3 

245 
2.53 
263 
261. 1 

189 
194 
186 
249 

77 

95-5 
78.5 
106.6 

28.3 
20.5 
30.2 
22,5 

22.3 
17. 1 
21.4 
17.7 

91 
8.4 

9 

7 

47.3 
34.8 
52.4 
43.8 

38 
28.5 
36.9 
33  0 

16.2 
12.6 
13.8 
12.9 

26.0 
27-5 
26.3 
26.7 

26.5 
27.7 
26.9 
26.7 

26.4 
26.0 
27.7 
26.3 

0° 

0° 

54.6° 
37  7° 

0° 

0° 
50.5° 
38.1 

0° 

0° 
36.3° 
36.3 

15.75 
17-4 
13.4 

14.0* 

16.2 
16.8 
12.7 
13-2' 

17.7 
16.9 
15- 1 
13- 6* 

*  The  proportion  of  the  total  steam  consumed  by  the  main  engine  was  assumed  to  be  the  same 
in  the  case  of  the  Texas  as  in  the  case  of  the  Delaware. 


TABLE   4 
H.M.S.  Argonaut,  Starboard  Engine 


R.P.M. 

Pressure  at 

engine 

gage 

Actual 
expansion  R^ 

I.H.P. 

M.R.P. 

Vacuum, 
inches 

Pounds  of 

steam  per 

I.H.P. 

74-7 
75 

76.7 
76 

168 

142 
78 
68 

16. 1 

135 

9-3 

8.5 

1907 
1922 
1929 
193 1 

16.4 
16.4 
16. 1 
16.3 

25 -5 
25 -5 
26.1 
26.2 

16.26 
16.68 
17.58 
17.72 

In  Fig.  10  the  steam  consumption  has  been  plotted  upon  mean 
referred  pressure  as  abscissae,  and  it  is  quite  evident  that  the 
Birmingham'' s  engines,  developing  their  maximum  power  with  a 
mean  referred  pressure  of  35  pounds  per  square  inch,  are  not  as 
economical  as  the  engines  of  the  Delaware  which  used  a  mean 
referred  pressure  of  over  52  pounds  per  square  inch.  The 
engines  of  the  Texas,  using  a  mean  referred  pressure  of  about  44 
pounds  per  square  inch,  are  not  as  economical  as  the  Delaware's 
at  full  power,  although  more  economical  at  low  power.  The 
greater  economy  of  the  Texas  at  low  power  is  probably  due  to 
the  use  of  higher  steam  pressure.     Table  4  taken  from  the  trials 


1 8        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

of  the  Argonaut  shows  the  effect  of  increasing  the  steam  pressure 
at  reduced  powers. 

The  Birmingham's  engines  would  have  been  much  more 
economical  at  maximum  power  if  superheated  steam  had  been 
used  and  if  the  cyhnders  had  been  of  such  a  size  that  the  mean 
referred  pressure  had  been  50  pounds  per  square  inch  instead 
of  36  pounds.     This  would  have  called  for  cylinders  of  about 


20 

\ 

y 

A=Argonaut 

B  =  BlRMINGHAM 

D— Delaware 
T=Texa3 

— 

19 

\ 

\ 

* 

18 

\ 

\ 

a. 

\ 

V 

•^ 

A 

17 

"cc" 

n\ 

y 

^ 

tMc 

sa 

p 

M 

\ 

V 

A 

^ 

16 

2 

-  < 
u 
»- 
CO 

-  OJ 

03 

_J 

\ 

\ 

s^ 

y 

■KE 

TEt 

j^ 

^ 

^ 

\ 

s, 

\ 

s 

"^ 

■~~J. 

/ 

\ 

UA 

^ 

. 

z 

\ 

V 

-^ 

15 

\ 

\A 

\ 

\ 

s 

-^ 

"^ 

13 

V, 

^^ 

^ 

^^ 

^ 

__^ 

^ 

V 

^ 

T 

— -. 

.^ — 

K^ 

U 

1 

10 

8  10  12  14  16  18  20  22  24  26  28  30  32  34  36  38  40  42  44  46  48  50  52 
M.  R.  P. 

Fig.  io. 

31  inches-48  inches  (2)  54  inches  instead  of  28|  inches-45  inches 
-(2)  62  inches  as  used. 

In  the  case  of  naval  engines  the  economy  at  reduced  power  is 
a  matter  of  great  importance,  as  the  cruising  speed  requires  only 
a  small  portion  of  the  maximum  power.  Under  these  conditions, 
if  it  is  desired  to  keep  the  cut-off  in  the  H.P.  cylinder  unaltered, 
an  engine  which  develops  its  maximum  power  with  mean  referred 
pressures  about  20  per  cent  less  than  those  given  in  Table  i  will 
be  more  economical  at  reduced  power,  but  the  economy  at 
maximum  power  will  suffer.  If  the  cut-off  in  the  H.P.  cylinder 
is  shortened  at  low  powers  to  enable  the  power  to  be  developed 


DETERMINATION  OF   CYLINDER   DIMENSIONS  19 

with  as  high  a  steam  pressure  as  possible,  the  engine  can  still 
use  the  higher  mean  referred  pressures  for  maximum  power  and 
be  economical  at  both  maximum  and  low  powers. 

In  the  case  of  engines  for  merchant  ships  the  economy  at  full 
power  is  of  most  importance  and  the  larger  mean  referred 
pressures  should  be  used. 

A  consideration  of  the  effect  of  these  varying  conditions  will 
show  that  it  is  hopeless  to  expect  such  a  simple  expression  as 
(2)  or  (6)  to  give  constant  values.  The  results  are  more  con- 
stant with  (6),  however,  and  that  formula  will  be  used  hereafter 
to  give  the  relation  between  P,,  M.R.P.o,  and  Ra. 

13.  Size  of  L.P.  Cylinder.  —  Since  the  mean  referred  pressure 
with  which  an  engine  develops  its  power  affects  the  steam 
economy  so  materially  it  is  best  to  start  the  design  by  assum- 
ing a  value  which  seems  desirable  under  the  conditions.  The 
quantities  with  which  we  will  start  the  design  will  be:  indicated 
horse-power,  piston  speed,  boiler  pressure,  mean  referred  pressure, 
and  back  pressure  in  L.P.  cylinder.  The  area  of  the  L.P.  cylinder 
will  be 

^  LH.P.  X  33.000  .,N 

""       P.S.  X  M.R.P.  '  ^^^ 

I.H.P.  =  indicated  horse-power, 

P.S.  =  piston  speed  in  feet  per  minute  suitable  for  t^-pe 
of  engine, 
M.R.P.  =  mean  referred  pressure  suitable  for  type  of  engine 

(see  Table  i). 

14.  Number  of  Expansions.  —  The  curves  of  Figs.  2,  4,  and  6 
enable  us  to  determine  the  number  of  expansions  which  will  give  • 
this   mean    referred    pressure.     These    curves    are   plotted    for 
saturated  steam  upon  values  of  M.R.P.o,  or  M.R.P.  -f-  P^. 

c-  '        zj       M.R.P.o  /P,V'  /A^ 

Smce  ^.___y     ,  (6) 

M.R.P.o 


H  =  ^^^:^^^x 


PO.6         '^    p  0.4' 

AT  TJ  P 
or  ^  X  RJ"-'  =      poe"  (saturated  steam).  (8) 


20        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


The  assumed  values  of  M.R.P.  and  Pq  enable  us  to  get  the 
value  of  M.R.P.o-  The  boiler  pressure  is  known  and  from  this 
Pi,  which  is  the  initial  pressure  absolute  in  the  H.P.  cylinder, 
can  be  found.  The  drop  in  pressure  from  the  boiler  to  the  H.P. 
cylinder  will  depend  upon  the  length  of  piping  and  speed  of 
steam.  At  maximum  power  this  drop  usually  varies  from  15 
to  30  pounds. 

If  the  curve  in  Fig.  4  marked  H  is  accepted  as  giving  average 
values  of  the  factor  H,  the  value  of  Ra  can  be  found  directly  from 
the  curve  marked  H.Ra^-^. 

15.  Size  of  H.P.  Cylinder.  —  The  size  of  the  H.P.  cylinder 
can  be  found  when  the  value  of  Ra  is  determined. 


Ra    = 


final  volume  of  steam 
initial  volume  of  steam 

{An  -  x)  {Ch  +  C/^) 
Al  =  area  of  L.P.  cylinder. 
Ah  =  area  of  H.P.  cylinder. 

X    =  ^  area  of  piston  rod. 
CIl  =  clearance  volume  of  L.P.  cylinder  expressed  as  a 

fraction  of  the  stroke. 
Cfj  =  cut-off  in  H.P.   cylinder  expressed  as  a  fraction 

of  the  stroke. 
CIh  =  clearance  volume  of  H.P.  cylinder. 


(A,  -  :r)  (i  +  Ck) 


(9) 


16.  Clearances.  —  The  values  of  CIh,  CIl,  and  Ch  will  have 
to  be  assumed.  It  is  good  practice  to  keep  the  clearances  as 
small  as  possible,  and  by  making  the  ports  horizontal,  using 
fairly  high  piston  speeds,  and  keeping  the  valves  close  to  the 
cylinder,  they  can  usually  be  made  about  as  follows: 


Piston  valves 

Flat  valves 

CIb  =  0. 16 
CIm  =  0.13 
CIl  =  0.12 

O.IO 
0.09 

DETERMINATION  OF   CYLINDER   DIMENSIONS 


21 


17.  Cut-offs.  —  C//  is  usually  from  0.7  to  0.85.  The  smaller 
C//  is  made,  the  larger  will  be  the  size  of  the  H.P.  cylinder  and 
the  smaller  will  be  the  ratio  between  the  H.P.  and  M.P.  cylinder 
volumes  for  a  given  Ra.     This 

will  cause  the  economical  cut- 
off in  the  M.P.  cylinder  to  be 
more  nearly  equal  to  C^.  Fig. 
II  shows  the  cylinder  ratios 
which  must  obtain  in  order  that 
the  cut-off  may  be  the  same  in 
all  cylinders.  There  is  no  par- 
ticular virtue  in  having  all  cut- 
offs the  same,  but  the  engine 
will  run  smoother  and  the  valve 
diagram  will  work  out  better  if 
the  cut-offs  are  at  least  0.65. 

18.  Sizes  of  Intermediate 
Cylinders.  —  The  size  of  the 
L.P.  cylinder  having  been  ob- 
tained from  the  power  to  be 
developed,  and  the  size  of  the 
H.P.  from  the  number  of  ex- 
pansions, we  can  place  between 
these  two  cylinders  as  many 
others  as  we  may  think  neces- 
sary. The  sizes  of  these  inter- 
mediate cylinders  are  usually 
made  in  accordance  with  the 
following : 


'40  50  60  70 

Percent  of  Cut-off  in  All  Cylinders 

Fig.  II. 


M.P.  cylinder  of  Triple 
I  St  M.P.  of  Quadruple 
2nd  M.P.  of  Quadruple 
ist  M.P.  of  Quintuple 


Am 

A 

Aim 

Ah 

Mm 

a7i 

Aim 


Am   ^  (Al]^ 
Ah        UhI  ' 

&■ 


(10) 
(loA) 
(loB) 


22        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

2nd  M.P.  of  Quintuple    ^  =  1^]' • 

Ah       \AhI 

3rd  M.P.  of  Quintuple     ^  =  (^V- 

etc. 

The  M.P.  cylinder  is  sometimes  made  smaller  than  the  above, 
but  in  doing  so  the  economical  cut-ofif  in  the  L.P.  is  made  very- 
short. 

19.  Stroke.  —  The  stroke  of  the  engine  is  usually  made  equal 
to,  or  a  little  greater  than,  the  diameter  of  the  M.P.  cyHnder. 
It  is  usually  made  some  one  of   the  following   quantities :  — 

//         //         i>         n      till //     ,^rt     .  „//    .Qit    ^    n    ^    I'    c^'t    f^fi^ii    „„// 

24' -27  -30  -33  -36  -39  -42  -45  -48  -51  -54  -60  -66  -72   . 
Naval  engines  rarely  use  a  stroke  greater  than  48  inches. 

20.  Superheat  Factor.  —  When  superheated  steam  is  to  be 
used  the  same  methods  will  be  employed  as  for  saturated  steam, 
but  another  factor  will  have  to  be  introduced  into  Formula  (8). 

It  can  be  seen  from  Fig.  7  that  the  mean  referred  pressure 
obtained  from  steam  of  a  given  pressure  decreases  as  the  amount 
of  superheat  increases.  In  Fig.  4  there  would  be  a  series  of 
curves  for  B.  under  the  curve  for  saturated  steam,  each  curve  for 
a  particular  degree  of  superheat.  Instead  of  drawing  these 
curves  and  taking  the  value  of  H  from  them  we  can  introduce 
into  Formula  (8)  a  factor  obtained  from  Fig.  7.  This  equation 
will  become 

M.R.P.o 


S'E  '  Ry  = 


P 


0.6 


.      H  -R'-'      M.R.P.o  ,     , 

s  is  Si  factor  obtained  from  Fig.  7. 

The  same  M.R.P.o  can  be  obtained  from  superheated  steam 
as  from  saturated  steam  if  a  smaller  number  of  expansions  is 
used.  In  discussing  the  best  M.R.P.  to  be  used  under  different 
conditions,  it  was  pointed  out  that  a  smaller  M.R.P.  could 
be  used  to  advantage  with  superheated  steam.  This  smaller 
M.R.P.  would  call  for  a  larger  number  of  expansions.  The  net 
result  of  decreasing  the  M.R.P.o  in  the  numerator  of  Formula 


DETERMINATION   OF    CYLINDER   DIMENSIONS  23 

(11)  and  using  a  factor  s,  less  than  unity,  in  the  denominator  is 
to  call  for  a  slightly  larger  number  of  expansions  when  super- 
heated steam  is  used. 

21.  Distribution  of  Power.  —  The  cut-offs  used  in  the  M.P. 
and  L.P.  cyhnders  will  affect  the  steam  economy  of  the  engine, 
the  amount  of  power  developed,  the  distribution  of  power,  and 
the  smoothness  of  running.  The  methods  for  determining  the 
cut-offs  which  will  give  maximum  economy  and  maximum  power 
have  been  given  above.  The  distribution  of  power  that  will 
result  from  given  cut-offs,  or  the  cut-offs  to  give  a  certain  dis- 
tribution of  power,  can  be  found  by  means  of  Fig.  12.  These 
curves  give  the  mean  of  the  results  obtained  from  engine  trials. 
The  abscissae  are  ratios  of  the  volumes  in  the  M.P.  and  L.P. 
cylinders  at  cut-off  to  the  volume  in  the  H.P.  cylinder  at  cut-off. 
The  ordinates  are  the  portions  of  the  total  work  developed  in  the 
preceding  cylinder  or  cylinders. 

It  will  be  noticed  that  the  curves  give  zero  work  for  a  volume 
ratio  of  0.5.  There  are  no  trial  results  from  which  this  part  of 
the  curve  can  be  determined  and  the  curves  were  made  to  pass 
through  that  point  somewhat  arbitrarily.  Theoretically  there 
would  be  zero  work  done  in  the  H.P.  cylinder  if  the  volume  at 
cut-off  in  the  second  cylinder  is  the  same  as  that  in  the  H.P. 
since  the  steam  would  be  brought  back  to  the  original  volume 
and  pressure.  There  would  be,  however,  a  considerable  amount 
of  initial  condensation  in  the  second  cylinder,  especially  if  the 
cut-off  is  short,  which  would  cause  the  pressure  at  cut-off  in  that 
cylinder  to  be  less  than  it  was  in  the  H.P.  cylinder,  and  a  certain 
amount  of  work  would  be  done.  It  was  arbitrarily  assumed 
that  zero  work  would  be  done  when  the  cut-off  volume  in  the 
second  cylinder  was  one-half  that  of  the  H.P.  cy Under  cut-off 
volume. 

22.  Example  of  Design.  —  The  method  of  design  will  be 
illustrated  by  means  of  an  example.  Suppose  that  30,000  I. H.P. 
is  to  be  developed  by  two  reciprocating  engines  and  two  low- 
pressure  turbines,  the  turbines  to  take  steam  from  the  low-pres- 
sure cylinders  at  about  17  pounds  absolute.  The  steam  will  be 
developed  at  a  pressure  of  275  pounds  gage  and  with  90°  of 


24        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


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DETERMINATION   OF    CYLINDER   DIMENSIONS  25 

superheat.     A  drop  of  20  pounds  in  pressure  and  30°  in  super- 
heat will  be  allowed  between  boilers  and  cyUnder. 

I.H.P.  =  7500,     Pi  =  270  pounds  absolute,     Pb  ==  18  pounds 
absolute, 

P.S.  =  1000  feet  per  minute,     CIh  =  0.12,     CIm  =  o.ii, 

CIl  =  o.io,     Ch  =  0.75. 
From  Table  i  the  M.R.P.  for  best  economy  will  be  about  48 

pounds. 

M.R.P.o  =  48  +  18  =  66  pounds. 

From  Fig.  7  the  superheat  factor  =  0.95. 

•••     H-R^'=^—^ -=2.41, 

270"-''  X  0.95 

i?a  =  6.35  (see  Fig.  4), 

^    ,  7i;oo  X  SS1000  .     , 

net  Al  =  ^-^ "^^ —  =5150  square  mches. 

1000  X  48 

If  two  low-pressure  cylinders  are  used,  net  Al  =  2575  square 
inches  each. 

(net^z,)(i  +CIl)    ^  ^  5150  X  i-i 

(net  Ah)  (Q  +  CIh)         '^^      0.87  (net  Ah) 
net  Ah  =  1025  square  inches, 
net  Am  =  ^^5150  X  1025  =  2300  square  inches. 

The  piston  rods  will  be  about  6  inches  diameter  and  the  half 
sectional  area  of  each  rod  equals  about  15  square  inches. 

Ah  =  1025  +  15  =  1040,  Dh  =  36.3",  use  36^", 

Am=  2300  +  15  =  2315,  Dm  =  54-3"»  use  54I'', 

Al  =  ^SIS  +  15  =  2590,  ^L  =  57-4",  use  57I". 
Stroke  =  48  inches. 

A  complete  investigation  of  the  effects  of  the  cut-off  in  the 
M.P.  and  L.P.  cylinders  upon  the  distribution  of  power  can  be 
made  by  calculating  the  distribution  for  30  per  cent,  50  per  cent, 
70  per  cent,  and  90  per  cent  cut-offs,  and  plotting  the  results. 
30  per  cent  cut-of  in  M.P.  cylinder 

(0.30-1-0.11)2319  ^  ^^^^ 

(0.75-1-0.12)1032 


26        THE  DESIGX  OF  MARINE  ENGINES  AND  AUXILIARIES 

According  to  the  curve  for  moderate  superheat  in  Fig.  12  this 
cut-off  volume  ratio  will  cause  8.5  per  cent  of  the  total  work 
to  be  developed  in  the  H.P.  cylinder. 

50  per  cent  ciit-of  in  M.P.  cylinder 

Cut-off  volume  ratio  =  1.06-^ —  =  1.58. 

0.41 

Per  cent  of  total  work  =  16. 
70  per  cent  cut-of  in  M.P.  cylinder 

Cut-off  volume  ratio  =  1.06^ —  =  2.09. 

0.41 

Per  cent  of  total  work  =  23. 
90  per  cent  cut-of  in  M.P.  cylinder 

Cut-off  volume  ratio  =  1.06^ —  =  2.6. 

0.41 

Per  cent  of  total  work  =  29.3. 
30  per  cent  cut-of  in  L.P.  cylinder 

„  ^    ^       ,  ^.         (0.^0+0.10)^516=; 

Cut-orf  volume  ratio  =  ^^ -^ — ^  =  2.30. 

0.87  X  1032 

Per  cent  of  total  work  =  25.6. 
50  per  cent  cut-of  in  L.P.  cylinder 

Cut-off  volume  ratio  =  2.30^ —  =  3-46. 

0.40 

Per  cent  of  total  work  =  38.3. 
70  per  cent  cut-of  in  L.P.  cylinder 

Cut-off  volume  ratio  =  2.30 —  =  4.60. 

40 

Per  cent  of  total  work  =  47.7. 
90  per  cent  cut-of  in  L.P.  cylinder 

Cut-off  volume  ratio  =  2.30 =  5-75- 

40 

Per  cent  of  total  work  =  55. 

Curves  A  in  Fig.  13  are  plotted  from  these  results.     The  cut- 
offs for  best  economy  will  be  as  follows: 


DETERMINATION   OF   CYLINDER  DIMENSIONS 


27 


Ti/r  T»  1-    J  n         2310  X  I. II 

M.P.  cybnder,  R  =  -^-^ =  2.23, 

1032  X  1. 12 

0.15  + =  0.60: 

2.23 

L.P.  cyKndcr,  R  =  ^'^^  ^  ^'^   =221, 
2319  X  I. II 

0.15  -{ ■  =  0.605. 

2.21 


75 

70 

65 

60 

55 

501-' 

45 

40 

35 

30 

25 

20 

15 

to 


10 


J-t-"' 

;=  :';:::::::::::::::::::::±;; 

a: 

UJ 

0 

Un 

Q. 
u. 
0 

_     ,_  _   __  —            - 

1- 
z 

UJ 

—  -'---  :;  _:::;,?' 

Lf                      urn 

n\                    -MT 

0 
cr 
tij 

'  1 1 1  J  M-rn'l  II 

UtT''-'-'- 

:;:^?  =  !:::±::::::;: 

.-,tX 

Xl 

d;;  =  !!±±::::::;±?-:::^ 

--  ?^ 

rfTf^ tS-"'^^^ 

""ii        _  ::;;  =  i':  Power  Developed 

X    ' .i'-'.'  --T-   IN  H. P.  Cylinder 

u 

.J'"" 

^Tl  ' 

;*>^-A 

.'           u>^ 

,•; 4,'^^ 

NT  OF  CUTrOFF 

::x,«'!:: 

r                           Perce 

20 


30 


40 


50      60 
Fig.  13. 


70 


80 


90 


100 


The  cut-offs  for  maximum  power  will  be: 

M.P.  cylinder  =  0.60  X  1.4  =  0.84, 
L.P.  cylinder  =  0.605. 

The  curves  of  Fig.  13  enable  us  to  determine  what  portion  of 
the  total  power  will  be  developed  in  the  different  cylinders  by 
these  cut-offs  or  any  others  that  we  may  care  to  use. 


28       THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


Per  cent  of  total  work  in 

M.P. 
cut-off 

L.P. 

cut-off 

H.P. 

M.P. 

L.P. 

(l) 

Max. 

economy.. 

o.6o 

0.605 

20 

24 

56 

(2) 

Max. 

power .... 

0.84 

0.605 

27-S 

16. 5 

56 

(,S) 

0.  76 

0.75 

25 

25 

SO 

(4) 

0.60 

0.53 

20 

20 

60 

The  cut-offs  given  in  line  (4)  seem  to  be  the  best  in  this  case. 
They  will  insure  that  the  engine  will  have  its  maximum  economy, 
and  the  engine  can  be  balanced  by  putting  the  two  L.P.  cylinders 
in  the  middle  of  the  engine,  and  the  H.P.  and  M.P.  cylinders  can 
be  placed  at  the  ends  of  the  engine  and  the  parts  made  lighter, 
since  each  develops  less  than  each  L.P.  cylinder. 

If  this  engine  were  to  work  with  a  back  pressure  of  4  pounds 
absolute  instead  of  18  pounds  absolute  the  value  of  Ra  would  be 
8.8,  and  the  cylinder  diameters  and  stroke  would  be 


31 


50' 


S7¥'  (2) 


48" 

The  broken  lines  in  Fig.  13  are  the  curves  for  this  engine  and 
it  can  be  readily  seen  that  the  usual  distribution  of  power, 
namely,  H.P.-30  per  cent,  M.P.-30  per  cent,  L.P.-40  per  cent, 
could  be  easily  obtained  with  these  proportions. 

23.  Steam  Consumption.  —  Fig.  14  gives  the  relation  be- 
tween M.R.P.4  (four  pounds  back  pressure  in  L.P.  cylinder), 

.    p 

pounds  of  steam  per  I.H.P.,  and  ratio  — ^.     There  seems  to  be 

Ra 

some  ground  for  the  statement  that  the  steam  per  I.H.P.  de- 

P 
creases  for  any  given  value  of  -^as  the  M.R.P.  is  increased. 

Ra 

Engine  tests  usually  determine  only  the  most  economical 
conditions  under  which  that  particular  engine  can  be  run.  The 
determination  of  the  most  economical  condition  under  which 
power  can  be  generated  would  necessitate  tests  where  a  certain 
M.R.P.  is  obtained  with  different  values  of  Pj  and  Ra.  Fig.  6 
shows,  for  instance,  that  a  M.R.P.q  of  50  pounds  can  be  obtained 
under  the  following  conditions: 


DETERMINATION  OF   CYLINDER   DIMENSIONS 


29 


P^ 

Pj 

Pi 

Ra 

Ra 

Pi 

Ra 

Ra 

140 

s-(>s 

24.7 

225 

8.40 

26.8 

160 

6.35 

251 

250 

925 

27.0 

180 

6.95 

25-9 

27s 

10 -35 

26.6 

200 

7-55 

26.5 

in 

in 
rsi 

CO 
u 

z 

Ul 

2 

0   - 

2 

LU 

ID 

0 

Compound  Engi 

3  Cyl.  Triples 

4  - 

S  "• 

in 

rr 

UJ 

_i 
Q. 

-^     J 

■>* 

CE 
0 

•>* 

13 
ft 

CSI 

" 

<  ^ 

• 

TT 

> 

0 

^Sl 

^ 

^d 

""• 

00 

"-      ■ 

CO 

^ 

2 

■H 

en 

s 

^ 

„ 

en 

CSJ 

-* 

^ 

m'". 

■  ■ 

I"- 

en 

0 

^  m 

■V 

0,  °? 

1'' 

" 

'      - 

on 

V 

» 

s 

^ 

'-<^ 

< 

■«l 

^ 

.3=- 

< 

:f=-' 

•to 

CM 

CO 

"^l 

« 

•< 

.^ 

*- 

[; 

CM 

- 

"< 

•  »"r 

■^^ 

s, 

0   10 

CN 

<» 

4  - 

t 

« 

a. 
0 

1 

CM 

"" 

^ 

"~n 

=: 

« 

s*^ 

a    , 

CM 

no 

f  ^ 

0. 

* 

^5^' 

' 

» 

= 

■ 

CO 

<^ 

:;; 

■ 

s 

•^ 

(D, 

<D| 

2 

c^ 

n 

[^ 

»• 

0 

cc 


•d'HI  a3d  IAIV31S  dO  "sai 
Fig.  14. 


30 


THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


It  seems  probable  that  some  one  of  these  conditions  would 
prove  more  economical  than  any  of  the  others.  A  complete 
investigation  made  in  this  way  with  different  sized  engines 
would  determine  under  what  condition  power  could  be  most 
economically  generated. 

24.  Distribution  of  Work  at  Reduced  Powers.  —  Fig.  12 
gives  the  distribution  of  work  when  the  engines  are  developing 
full  power.     As  the  power  is  reduced  the  distribution  may  change 

Lake  Freighter  Pennsylvania. 

Vac.  =  26" 
100 


Max.  R.P.IVI.  =  80 

y 

r 

<^^ 

y 

y 

D. 

.< 

W 

y 

Cl 

/ 

.V 

-^^ 

S 

u 
n 

^ 

V 

u. 

1- 
z 

UJ 

y 

<^ 

/ 

0 
tr 

UJ 

Q. 

A 

/ 

0 
u 

-J 
< 

0 
CO 

1' 

/CT" — 

^RCE 

r — i      1      1 

MT  OF  Max.  Power. 

1 

50-2 


40 


30 


20 


10 


40 


35  1, 


10   20 


30 


40    50 


60 


70 


30 

25 

20 
80   90   100 


bo 


o  < 


u  o 
a  Q 


Fig.  15. 


somewhat,  as  shown  by  Figs.  15  to  18.  The  results  from  which 
these  figures  were  plotted  were  obtained  from  engines  running 
with  fixed  cut-offs,  the  power  being  reduced  by  throttling  the 
steam  or  reducing  the  boiler  pressure.  It  will  be  noticed  that 
in  general  the  percentage  of  work  developed  in  the  L.P.  cylinder 
decreases  as  the  initial  pressure  falls. 


ioo 

90 
80 
70 
60 
50 
40 
30 
20 
10 


Vac.  =  27" 


90    Superheat. 


Max.  R. P.M.  =  124^ 

^^ 

yjA 

>^ 

<^ 

^ 

/ 

r 

d1 

of 

y 

^ 

y 

^ 

/ 

2 

CL 

y 

y 

.'T^ 

/^ 

5^* 

> 

UJ 

CC 

ce 

\ 

> 

k 

O 
u. 

1- 
z 

\ 

V 

/ 

o 

tr 

UJ 

Q. 

A 

r 

^ 

Li. 

o 

LJ 

_I 

// 

^ 

L 

' 

H 

o 

/ 

/ 

"M — 

/ 

f 

^'ERCE 

NT  OF 

VlAX.  F 

=  OWEF 

100 
90 
80 
70 
60 
60 
40 
30 
20 
10 


10        20        30        40 
Fig.  i6. 
Vac.  =  27" 


50        60        70        80       90 
U.  S.  S.  Michigan. 

Superheat. 


20 
100 


Max.  R. P.M.  =  128 

^ 

/^ 

T' 

Q." 

^ 

^ 

/ 

^ 

CC 
2 

X 

^ 

y 

^ 

a 

/ 

/ 

t 

.f 

V 

> 

UJ 

CC 
or 

/ 

J 

/ 

\. 

o 

u. 

1- 
z 

UJ 

A 

V 

_L 

o 

UJ 

a. 

^  u.        '^ 
O 

UJ 

^^ — 'a 

k 

'^ 

Z 

■   ■ 

— — 



__H__ 





- 

O       " 
CO 

_ 



-"^ 

M 

^ERCE 

gT  OF  Max.  F 

^OWER 

■ 

^  9 


fe5 
H  I 
u.  o 
o   < 

25    z  z 


UJ   C 


10        20        30      .40        50        GO        70        80        90       100 
Fig.  17.     U.  S.  S.  Delaware. 


40 

^ 

a:  a. 

0    Ul 

5S 

35 

65 

30 

1-  I 

ir     0 

0,1^ 

?5 

^? 

n  UJ 

rr  ^ 

UJ   0 

CL  CJ 

31 


THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


,100 


90 


80 


70 


60 


50 


40 


30 -t 


20 


10 


U^S.S.  So.  Carolina. 
Vac.  =  27.7" 


IVTax.  R.P.M.  =  1  28^'--''"^X 

CL 

^^ 

/ 

V 

/ 

y 

V 

'a 

/ 

CL 

/ 

/ 

/ 

J' 

IT 

/ 

/ 

V 

V 

// 

"-^ 

o 

u 

A 

'/ 

O 

LJ 
_J 
< 

^K^ 

^ 

o 

CO 

y 

^ 

^■^v..^ 

_w\ 

^x---^ 

~~~~ — .^ 

F 

1       1 

^ERCENT  OF  Max.  Power. 

1 

10 


20    30    40    30 


60 


70 


80 


40 
35 
30 

25 

20 
90   100 


Fig.  i8. 


100 


90 


80 


70 


60 


50 


40 


.-^^TT 

- 

^^^ 

^ 

□. 

^ 

F. 

sl.D. 

^5^ 

^ 

^^ 

-5  — 
5 

^ 

^.iXr:   A^  /■  1  ' 

~H. 

^ 

/iT  Lf 

X 

1  ' /\l 

IX^ 

< 

"bly- 

^1^ 

0 

"  ■ 3 1" 2 

-  ^~\ 

. 

z 

LiJ 

(5 

N  D 

R.P.M.I 

OTA   ''°"l 

q: 

LLl 
Q. 

P.= Florida.  .. 
HI=Henle'y-_- 

■--1 

_364 
.  637 

-X  t-- 

?-- 

.1,1        1 

J    — JOIIt^TT 

— 

.960 

1  1 1 1 1 

rr  ~  ^ 

^fJJU 

— ~m 

B     / 

JM   P 

1    il/'     ^"- 

PERCE 

NT  C 

)F  MA 

XIML 

DWE 

R 

10  20  30  40  50  60  70  80  90  100 
Fig.  19. 


DETERMINATION   OF   CYLINDER   DIMENSIONS  33 

25.   Variation  of  Revolutions  and  M.R.P.  at  Reduced  Power. 

—  It  is  interesting  to  note  the  manner  in  which  the  mean  re- 
ferred pressure  and  number  of  revolutions  per  minute  vary  as 
the  power  is  decreased.  The  revolutions  decrease  much  less 
rapidly  than  the  mean  referred  pressure.  The  greater  the  maxi- 
mum number  of  revolutions,  the  m.ore  rapid  the  rate  of  decrease 
of  the  revolutions.  This  is  shown  by  comparing  Fig.  1 5  in  which 
the  maximum  number  of  r.p.m.  was  80  with  Fig.  16  in  which  the 
maximum  number  of  r.p.m.  was  124.  This  is  also  shown  more 
clearly  in  the  case  of  boats  with  turbines.  In  Fig.  19  we  have 
maximum  revolutions  per  minute  ranging  from  280  to  960,  and 
the  rate  of  decrease  of  revolution  with  power  is  more  rapid  with 
the  higher  revolutions. 

In  the  case  of  the  battle-ship  engines  shown  in  Figs.  16  to  18 
the  mean  referred  pressure  at  half  power  is  60  per  cent  of  that 
at  full  power.  In  other  words  a  decrease  of  power  of  10  per  cent 
is  accomplished  by  a  reduction  of  mean  referred  pressure  of  8 
per  cent  and,  approximately,  a  2  per  cent  reduction  of  revolu- 
tions. 


SECTION  II 
DESIGN  OF  ENGINE  PARTS 

WORKING   STRESS   FACTORS 

26.  Effect  of  Character  of  Load.  —  The  working  stress  factors 
to  be  used  in  the  design  of  the  different  parts  will  depend  upon 
the  character  of  the  load  to  which  any  part  is  subjected  and  upon 
the  construction  of  the  part.  There  are  three  kinds  of  load, 
steady,  intermittent,  and  alternating.  The  steady  load  is  one 
which  is  appHed  in  an  appreciable  length  of  time,  causing  tension 
or  compression  of  an  unchanging  amount.  The  intermittent 
load  is  one  which  is  applied  more  or  less  suddenly  and  produces 
tension  or  compression  of  a  varying  amount.  The  load  may 
vary  from  a  maximum  to  zero,  or  to  a  minimum  other  than  zero. 
The  smaller  the  range  of  variation  the  more  nearly  the  load 
approaches  a  steady  load.  The  alternating  load  is  of  such  a 
character  as  to  cause  the  stress  to  change  alternately  from  ten- 
sion to  compression. 

It  has  been  found  by  experiment  that  a  piece  of  metal  which 
has  enough  sectional  area  to  stand  a  certain  steady  load  for  an 
indefinite  time,  will  fail  after  a  while  if  the  load  is  intermittent 
and  varies  from  a  maximum  to  a  minimum,  and  will  fail  much 
sooner  if  the  load  is  alternating.  The  relative  destructiveness 
of  the  three  kinds  of  load  is  about  in  the  ratio  i,  2,  3.  A  piece 
of  metal  which  has  enough  area  to  carry  a  certain  steady  load 
indefinitely  must  have  the  load  reduced  to  one-half  if  it  becomes 
intermittent,  and  reduced  to  one-third  if  the  load  becomes 
alternating. 

27.  Working  Stress  Factors.  —  Working  stress  factors  are 
usually  based  upon  the  ultimate  strength  of  the  material.  If 
the  ultimate  strength  were  used  as  the  working  stress  the  part 
would  stand  only  one  application  of  the  load.     If  the  load  is  to 

34 


DESIGN   OF   ENGINE   PARTS  35 

be  applied  continually  the  working  stress  must  not  exceed  the 
elastic  limit,  the  limit  of  the  stress  to  which  a  material  may  be 
subjected  and  have  the  strain,  or  deformation,  proportional  to 
the  stress. 

The  elastic  limit  varies  for  different  grades  of  steel  but  for  the 
steel  used  in  marine  engines  it  is  about  62  per  cent  of  the  ultimate 
strength.  This  would  require  the  use  of  a  minimum  working 
stress  factor  of  1.6  for  steady  loads,  3.2  for  intermittent  loads, 
and  4.8  for  alternating  loads.  It  is  rarely  possible  to  figure 
exactly  the  load  to  which  a  part  will  be  subjected  and  we  cannot 
be  sure  that  the  elastic  limit  will  always  be  0.62  of  the  ultimate 
strength;  for  these  reasons  it  is  usual  in  land  practice  to  apply  a 
further  factor  of  2.  This  gives  3.2,  6.4,  and  9.6  as  the  working 
stress  factors  for  the  three  kinds  of  load. 

In  marine  practice  it  is  usual  to  increase  the  factor  to  2.5  since 
the  parts  are  subjected  to  loads  of  greater  uncertainty,  due  to 
the  rolling  and  pitching  of  the  vessel,  and  also  because  a  break- 
down at  sea  is  accompanied  by  greater  danger  than  one  on  land. 
The  factors  for  engines  of  the  merchant  marine  are  thus  in- 
creased to  4,  8,  and  12  for  steady,  intermittent,  and  alternating 
loads. 

The  factors  for  naval  engines  need  not  be  as  large  as  for  mer- 
chant engines  since  the  latter  are  worked  to  nearly  their  maxi- 
mum capacity  all  the  time,  while  naval  vessels  are  ordinarily 
cruising  around  at  a  speed  which  calls  for  only  10  or  15  per  cent 
of  the  maximum  power  of  the  engines.  In  the  case  of  the  latter 
the  parts  can  be  designed  with  lower  factors  —  about  6  for 
intermittent  and  9  for  alternating  loads.  The  factor  will  be 
very  large  for  cruising  powers  and  yet  will  not  be  so  small  for 
the  short  time  that  the  engine  works  at  full  power  as  to  reduce 
the  life  of  the  engine  to  any  great  extent.  Advantage  is  not 
taken  of  this,  however,  in  all  classes  of  naval  engines  and  some 
of  the  engines  of  the  larger  battleships  are  designed  with  as  large 
factors  as  those  of  the  merchant  marine. 

In  the  design  of  certain  parts  such  as  the  piston  rod,  connecting 
rod,  and  eccentric  rods,  allowance  must  be  made  for  stresses 
introduced  by  lack  of  alignment.     As  the  different  pins  and 


36        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

bearings  wear  the  alignment  may  be  destroyed  and  the  loading 
may  become  eccentric.  In  the  case  of  such  parts  it  is  usual  to 
increase  the  working  stress  factor  50  per  cent  to  allow  for  these 
conditions. 

There  is  practically  no  part  of  a  marine  engine  which  is  sub- 
jected to  a  steady  load  —  hence,  as  low  a  factor  as  4  would  never 
be  used.  The  nearest  approach  to  a  steady  load  is  the  load  con- 
dition which  exists  in  the  receiver  pipes  between  cyhnders,  and 
in  the  line  shafting  of  balanced  engines.  In  these  parts  the  load 
is  intermittent,  varying  from  a  maximum  to  something  more 
than  half  the  maximum,  and  a  factor  as  low  as  6  may  be  used. 
It  should  be  borne  in  mind  that  the  working  stress  factors  of  8 
for  intermittent  and  12  for  alternating  loads  are  used  for  the 
purpose  of  gi\'ing  the  working  parts  a  long  life,  and  that  oc- 
casional loads  of  such  a  magnitude  as  to  reduce  the  factor  to  3 
can  be  carried  by  the  parts  without  injuring  the  material. 

28.  Threaded  Parts.  —  Certain  parts  should  be  designed 
with  larger  factors  than  those  given  above,  due  to  the  manner 
of  their  construction.  Bolts  and  studs  are  subjected  to  inter- 
mittent loads,  but  due  to  the  presence  of  threads  the  area  at  the 
root  of  the  threads  is  weaker  than  the  same  area  would  be  in  a 

TABLE  5 
Working  Load  for  Bolts 


Diam. 

Area  at 

No. 
of 

th'ds 

Working  load 

Diam. 

Area  at 

No. 

of 

th'ds 

Working  load 

root 

Merchant 

Naval 

root 

Merchant 

Naval 

3 

4 

.302 

10 

990 

1,650 

3 

5.63 

4 

33.800 

56,300 

i 

.419 

9 

1,410 

2,350 

3i 

6.73 

4 

40,400 

67,300 

I 

■55 

8 

2,060 

3,150 

3i 

7-9 

4 

47.400 

79,000 

li 

.694 

7 

2,670 

4,050 

31 

9.  21 

4 

55.200 

92,100 

li 

.891 

7 

3.520 

5,400 

4 

10.6 

4 

63.500 

106,000 

i^ 

I    057 

6 

4.250 

6,500 

4i 

12. 1 

4 

72,500 

121,000 

I* 

1.294 

6 

5. 360 

8,300 

Ah 

13-68 

4 

82,100 

136,800 

It 

1515 

5i 

6,450 

10,000 

Ai 

1536 

4 

92,100 

153,600 

If 

1.746 

5 

7.625 

11,800 

5 

17.2 

4 

103,500 

172,000 

li 

2.051 

5, 

9,170 

14,400 

5^ 

21.05 

4 

126,400 

210,500 

2 

2.302 

4i 

10,650 

16,800 

6 

25-3 

4 

152,000 

253,000 

2i 

3  023 

4* 

14,800 

23,500 

6i 

30 

4 

180,000 

300,000 

2h 

3   719 

4 

19,400 

31,200 

7 

35 

4 

210,000 

350,000 

2i 

4.622- 

4 

25,700 

42,000 

DESIGN  OF  ENGINE   PARTS  37 

perfectly  plain  bar.  In  small  bolts,  moreover,  a  considerable 
initial  stress  will  be  present  due  to  the  torsion  to  which  they  are 
subjected  when  the  nuts  are  set  up.  These  two  conditions  make 
it  necessary  to  increase  the  factor  to  10  in  the  case  of  all  bolts  3 
inches  in  diameter  and  over,  and  in  small  bolts  the  factor  should 
increase  as  the  diameter  decreases,  becoming  about  16  for  a  bolt 
I  inch  in  diameter.  Table  5  gives  the  loads  that  various  sized 
bolts  can  carry  when  the  steel  has  a  tensile  strength  of  60,000 
pounds  per  square  inch. 

29.  Column  Formula.  —  The  sizes  of  piston  rods,  connecting 
rods,  and  steel  columns  should  be  determined  by  means  of  a 
column  formula.  These  parts  should  all  be  considered  as 
columns  with  round  or  pin  ends.     Many  formulae  for  columns 

are  based  upon  the  value  of  -,  or  ratio  of  length  to  radius  of 

gyration  of  cross  section.     This,  however,  is  not  a  convenient 
form  for  engine  work,  and  for  that  reason  the  following  formulae 
have  been  devised: 
Solid  rods  or  columns: 


E 
Hollow  rods  or  columns: 


D2  ^  y/L8|C^  +  i^  +  F.  (12) 


D2   ^  ^lA^  +  /72  +   (2  /7  +  ^2)  J2  4.  p  (j3) 

D  =  diameter  in  inches  of  rod  at  middle  of  length. 
C  =  ultimate  strength  of  material  in  pounds  per  square 
inch. 

/  =  length  of  column  in  inches. 
E  =  modulus  of  elasticity  of  material. 

d  =  internal  diameter  of  hollow  column. 

W  =  maximum  load  upon  column  in  pounds. 
n  =  working  stress  factor,  to  be  determined  by  character 
of  load  and  construction  of  part. 


38        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


These  formulae  are  good  for  steel,  iron,  composition,  or 
wooden  columns,  and  the  following  values  of  E  and  C  should  be 
used: 


Material 

E 

C 

Steel 

Wrought  iron 

Cast  steel 

30,000,000 
28,000,000 
30,000,000 

13,000,000 

13,000,000 
2,000,000 
2,000,000 
1,700,000 
1,600,000 
1,400,000 

60,000-95,000 
48,000 

Cast  iron 

Composition 

Oak 

Yellow  pine 

Oregon  pine 

Spruce  and  ash 

White  pine 

\  15,000-20,000  (tension) 
\  100,000    (compression) 
40,000-60,000 

8,500  (compression) 
8,000  (compression) 
5,700  (compression) 
7,200  (compression) 
5,400  (compression) 

30.  Hollow  Columns.  —  In  naval  engines  it  is  often  desirable 
to  make  all  piston  and  connecting  rods  of  the  same  outside 
dimensions,  but  to  bore  out  the  rods  which  carry  the  lighter 
loads  and  thus  get  the  necessary  difference  in  weights  of  re- 
ciprocating parts  to  give  good  balance.  In  this  case  the  value 
of  F  should  be  found,  using  the  lower  value  of  W  for  the  cylinders 
developing  the  lesser  horse-power.  This  value  of  F  and  the 
value  of  D  found  for  the  other  cylinders  can  be  introduced  in 
the  following  equation  to  get  the  diameter  d  for  the  bore: 


J2    =  \J  J)A    _    ^-pjyi    _   h^lCR  j^  p2 


(14) 


The  relation  of  Formula  (12)  to  others  in  use  is  shown  in  Fig. 
20.  All  the  curves  are  drawn  for  steel  of  60,000  pounds  tensile 
strength,  and  a  working  stress  factor  of  4.  It  ^\dll  be  seen  that 
Formula  (12)  gives  results  agreeing  very  closely  with  the  Pen- 
coyd  tables  up  to  a  value  of  /  -i-  r  of  125,  and  from  there  on  the 
results  agree  with  the  tables  used  by  the  Bureau  of  Construction 
and  Repair  of  the  U.  S.  Navy. 

31.  Bearing  Pressures.  —  It  is  usual  to  figure  the  bearing 
surface  of  pins  and  shafts  as  equal  to  the  length  of  the  surface 
multiplied  by  the  diameter  of  the  pin  or  shaft.  The  pressure 
allowed  must  be  low  enough  to  keep  the  bearing  cool,  and  varies 


DESIGN  OF  ENGINE   PARTS 


39 


with  the  conditions  and  the  possibility  of  artificial  cooUng. 
When  there  is  no  motion  between  two  parts  the  pressure  can  be 
very  large,  but  as  the  extent  of  the  motion  between  them  in- 
creases, the  pressure  allowed  decreases.  Since  it  is  a  question 
of  keeping  the  bearing  cool,  we  can  deal  with  the  mean  unit 
bearing  pressure,  as  the  maximum  will  occur  generally  but  for 
an  instant.     In  some  cases,  however,  it  is  more  convenient  to 


22000 

20000 

18000 

16000 

14000 

12000 

10000 

8000 

6000 

4000 

2000 

0 


9 Pencoyd  Tables 

Tables  of  Bureau  of 

Construction  &  Repair,  U. 

Formula  (12) 


280     300 


deal  with  the  maximum  pressure  to  avoid  confusion.  The 
pressures  allowed  upon  the  different  surfaces  are  shown  in  Table 
6.  All  but  two  of  the  surfaces  are  figured  for  maximum  loads, 
as  these  loads  are  used  in  the  design  of  other  parts  and  it  is  less 
confusing  to  deal  with  but  one  load.  It  will  be  noticed  that 
those  surfaces  which  have  but  little  relative  motion  have  the 
greatest  unit  pressure  allowed  upon  them,  while  those  with  more 
motion  have  a  lower  unit  pressure.  The  determination  of  the 
loads  coming  upon  the  different  surfaces  will  be  taken  up 
later. 


40        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


TABLE   6 


Using  mean  loads 

Merchant 

Naval 

Crank  pin 

Main  bearings: 

ist  cylinder 

2nd  cylinder  for'd  bearing 

2nd  cylinder  aft.  bearing. 

3rd  cylinder  for'd  bearing. 

3rd  cylinder  aft.  bearing.  . 

4th  cylinder  for'd  bearing. 

4th  cylinder  aft.  bearing. . 

pounds 
200  to  250 

150  to  200 
200  to  250 
250  to  300 
300  to  325 
325  to  350 
350  to  375 
375  to  400 

pounds 
300  to  350 

250  to  300 
300  to  350 
350  to  400 
400  to  425 
450  to  500 
500  to  525 
550  to  600 

Using  maximum  loads 

Slipper  guide 

Crosshead  pins 

Link  block  pin 

Link  block  gibs 

Eccentric  rod  pins 

Drag  rod  pins 

Eccentrics 

Thrust  collars 

pounds 

50  to  70 

850  to  1000 

750  to  1000 

250  to  400 

700  to  950 

500  to  700 

75  to  150 

50  to  80 

pounds 
80  to  100 

1000  to  1200 
850  to  1200 
350  to  500 
900  to  1 100 
700  to  800 
150  to  200 
80  to  100 

SHAFTING 

32.  Types  of  Shafting.  —  There  are  four  kinds  of  shafts  used 
in  transmitting  the  power  of  the  engine  to  the  propeller;  the 
propeller  shaft,  the  line  shaft,  the  thrust  shaft,  and  the  crank 
shaft.  The  crank  shaft  is  subjected  to  twisting  and  bending, 
the  thrust  shaft  to  twisting,  the  line  shaft  to  twisting,  and  the 
propeller  shaft  to  both  twisting  and  bending. 

It  is  usual  to  figure  the  size  of  the  crank  shaft  from  the  twisting 
and  bending  forces  acting  upon  it,  and  then  to  base  the  sizes  of 
the  other  shafts  upon  the  crank  shaft. 

There  are  two  types  of  crank  shaft  in  use  for  marine  engines, 
the  "sohd  forged"  and  the  ''built  up."  The  "solid  forged"  is 
used  mainly  for  naval  engines  and  for  fast  yachts,  where  weight 
must  be  saved.  The  shafting  is  usually  made  hollow  and  the 
steel  is  high  grade  and  oil  tempered,  in  consequence  of  which 
the  cost  is  high.  The  "built  up"  shaft  is  hea\der,  but  since  it  is 
composed  of  a  number  of  small  forgings  it  can  be  made  more 


DESIGN  OF   ENGINE   PARTS  41 

cheaply  than  the  solid  forged.  The  "built  up"  type  is  common 
to  engines  of  the  merchant  marine.  There  is  an  intermediate 
type  in  which  the  crank  pin  and  webs  are  in  one  forging. 

33.  Equivalent  Twisting  or  Bending  Moments.  —  The  stress 
developed  at  the  last  bearing  in  the  crank  shaft  by  the  twisting 
and  bending  to  which  it  is  subjected  can  be  calculated  by  find- 
ing either  the  equivalent  twisting  moment  or  the  equivalent 
bending  moment  which  will  produce  a  stress  equal  to  that  pro- 
duced by  the  combined  twisting  and  bending. 

If  the  equivalent  twisting  moment  is  desired  the  following 
formula  can  be  used: 


T,^B-{-Vr'-{-B\  (15) 

If  the  equivalent  bending  moment  is  desired  the  following  formula 
can  be  used: 


B,  =  0.35  B  -f  0.65  Vr  +  B\  (16) 

B  =  maximum  bending  moment  acting  upon  shaft. 
T  =  maximum  twisting  moment  acting  upon  shaft. 

34.  Mean  Twisting  Moment.  —  The  mean  twisting  moment 
acting  upon  the  shaft  will  be 

I  =  IHP-  X  33,°°°  X  o 

2irn 

I.H.P.  =  total  indicated  horse-power  of  engine. 
n  =  revolutions  per  minute. 

The  relation  between  the  mean  twisting  moment  and  the 
maximum  can  be  determined  by  analyzing  the  results  obtained 
from  engines  which  have  been  built.  In  any  such  computations 
the  effect  of  inertia  should  be  considered,  as  the  maxima  obtained 
by  disregarding  inertia  effects  will  be  considerably  smaller  than 
if  inertia  is  taken  into  account,  especially  in  the  case  of  three- 
crank  engines.  When  the  cranks  are  at  180°  or  at  90°  the 
inertia  effects  are  nearly  balanced.  The  importance  of  con- 
sidering inertia  is  shown  by  the  following  table,  which  gives 
results  of  calculation  made  upon  certain  engines: 


42        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

TABLE  7 


Boston 

3  crank 

low  leading 


U.S.S. 

Monterey 

3  crank 

high  leading 


U.S.S. 

New  York 

3  crank 

high  leading 


U.S.S. 

Olympia 

3  crank 

low  leading 


Siberia 
4  crank 


I.H.P.  X  33,ooo 


(i) 


2  irrn 

Max.  turning  force, — 
inertia  forces  in- 
cluded    (2) 

^      (3) 
(i)       ^^^ 

Max.  turning  force,  — 
without      inertia 
forces.     (4) 

(4) 
(i) 
(2) 
(4) 


72,000 

101,500 

1. 41 

84,000 

1. 17 
1 .  21 


72,000 
109,000 

93.500 

1-3 
1.16 


102,500 

145,000 

1 .42 

125,250 

1 .  22 
1. 16 


101,000 
279,000 

1-55 
233,000 

1 .29 
1 .  20 


179,000 
245.500 

1-37 
240,000 

1-34 


The  maximum  forces  were,  on  the  average,  about  18  per  cent 
larger  for  three-crank  engines  when  inertia  was  considered  than 
when  it  was  neglected. 

35.  Maximum  Twisting  Moment.  —  The  maximum  twisting 
moment  can  be  obtained  from  the  mean  twisting  moment  by 
use  of  certain  factors: 


I.H.P.  X  33,000  X  12 


(18) 


T  =  ct 

2  tU 

c  =  2.0,  single-crank  engine 
=  1.67,  two-crank  engine 
=  1.5,  three-crank  engine 
=  1.35,  four-crank  engine. 

The  crank  shaft  will  be  subjected  to  a  maximum  bending 
moment  at  the  last  bearing,  and  an  investigation  of  a  number 
of  cases  showed  that  the  maximum  bending  occurred  at  practi- 
cally the  same  time  as  the  maximum  twisting.  The  same  forces 
which  are  acting  to  produce  the  maximum  twisting  moment  are 
acting  to  produce  bending.  These  forces  are  —  the  thrust  of  the 
connecting  rod  of  the  last  cylinder;  the  rotative  force  trans- 
mitted through  the  crank  pin  from  the  forward  cylinders;  the 
centrifugal  force  arising  from  the  rotation  of  the  crank  webs, 


DESIGN   OF   ENGINE   PARTS  43 

crank  pin,  and  lower  part  of  the  connecting  rod;   the  weight  of 
the  reciprocating  parts  of  the  last  cylinder. 

36.  Maximum  Bending  Moment.  —  The  force  which  pro- 
duces maximum  bending  was  found  upon  investigation  to  be 
about  0.8  of  the  force  producing  the  maximum  twisting  moment 
in  the  case  of  three-cylinder  engines,  and  equal  to  the  above 
force  in  the  case  of  four-cylinder  engines. 

It  will  be  assumed  that  the  bending  moment  upon  the  crank 
shaft  will  be  given  by  the  formula: 

.       ^  =  T-  ^''^ 

T  .  . 

W  =  0.8  —  (three-cylinder  engines) 
r 

T 

=  —  (four-cylinder  engines). 
r 

7  =  length  of  crank  arm  in  inches. 

/  =  distance    from  center   to   center  of  bearings  of   last 

cylinder 

=  0.7  diameter  of  L.P.  cylinder  (three-cylinder  Triples, 

and  Quadruples) 

=  0.85    to   0.95    diameter   L.P.   cylinder   (four-cyhnder 

Triples,  merchant) 

=  0.8    to    0.85    diameter    L.P.    cylinder    (four-cylinder 

Triples,  naval). 

37.  Shaft  Diameter  from  Equivalent  Twisting  Moment.  —  If 
the  equivalent  twisting  moment  is  to  be  used  in  finding  the  stress 
the  formula  will  be 

^       Ip 

r  =  radius  of  shaft  =  —  • 
2 

Ip  = (soHd  shafts) 

32 

=  ""  ^^'  ~  "^'^  (hollow  shafts). 
32 

.      /_   i^Ti 


44        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

or  Z)  =  1.72  Y  y  (solid  shaft).  (20) 

If  the  diameter  of  hole  in  hollow  shaft  =  d  =  cD, 

When  the  bending  and  twisting  moments  are  taken  as  above 
a  working  stress  factor  of  8  can  be  used.  A  number  of  shafts 
whose  diameters  conformed  to  Lloyd's  rules  were  analyzed  by 
this  method  and  the  stresses  varied  from  6600  pounds  per  square 
inch  to  8800  pounds  per  square  inch,  with  an  average  value  of 
7500  pounds  per  square  inch. 

In  naval  engines  where  steel  of  95,000  pounds  ultimate  strength 
is  used  the  working  stress  can  be  12,000  pounds  per  square  inch. 

38.  Shaft  Diameter  from  Equivalent  Bending  Moment.  — 
If  the  equivalent  bending  moment  is  used  the  formula  for  stress 
will  be 

^        I 

D 
r  =  —■ 

2 

I  = •  (solid  shaft) 

64 

=  '^^^  -  ^')  (hollow  shaft). 
64  _ 

D  =  2.17  V  y  (soUd  shaft)  (22) 

=  2.17  \7,,    ^\,  (hoUow  shaft).  (23) 

^  /  (i  -  C) 
diameter  of  hole 
'  =  D 

The  same  shafts  mentioned  above  when  analyzed  by  this 
method  gave  stresses  ranging  from  7900  pounds  per  square  inch 
to  10,500  pounds  per  square  inch,  with  an  average  of  9000  pounds 
per  square  inch.  This  would  mean  a  working  stress  factor  of 
about  7. 


DESIGN  OF  ENGINE   PARTS  45 

In  naval  engines  a  stress  of  14,000  pounds  per  square  inch 
would  be  permissible. 

39.  Coupling  Bolts.  —  The  different  sections  of  crank  shaft 
and  line  shaft  are  bolted  together  at  the  coupHng  flanges  by  bolts 
of  such  a  size  that  their  shearing  resistance  is  equal  to  the  shear- 
ing resistance  of  the  shaft. 

In  the  case  of  the  shaft 


/  = 

Tr 

^  Ip 
T 

f" 

16  T 

16 

In  the 

case 

of  the 

coupling  bolts 

T  = 

■-  fJn 

4 

•'• 

T 

=  Jn 

4 

/  =  unit  shearing  stress  in  shaft  and  bolts. 
T  =  maximum  twisting  moment  in  shafting. 
D  =  diameter  of  shafting. 

d  =  diameter  of  coupling  bolt  at  face  of  coupling. 
/  =  radius  of  pitch  circle  of  coupUng  bolts. 

=  about  0.7  D. 
n  =  number  of  coupling  bolts,  usually  6  for  three-crank 
engines  and  8  for  four-crank  engines. 

Since  the  shearing  stress  /  and  the  maximum  twisting  moment 

T  . 
T  are  the  same  for  bolts  and  shaft,  the  quantity  —  is  constant. 

tZ)^  _  Jmrd? 
16  4 

d=- v/-^ (soKd  shaft) .  (24) 

2   '  nJ 

2  ^  nJ 

inside  diameter  of  shaft. 

c  = 


outside  diameter  of  shaft. 


46        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

The  coupling  bolts  are  usually  tapered  from  end  to  end  at  the 
rate  of  i  inch  per  foot.  Where  the  nut  is  attached  at  the  smaller 
end  the  diameter  can  be  reduced  by  an  amount  varying  from  j 
inch  to  ^  inch.  In  the  crank  shaft  these  nuts  serve  merely  to 
keep  the  bolt  in  place.  In  the  hne  shaft  the  area  at  the  root  of 
the  threads  of  the  bolts  must  be  sufficient  to  take  the  pull  of  the 
propeller  when  the  engine  is  reversed. 

40.    Sizes  of  Crank  Shaft  Parts.  —  (See  Fig.  21.) 


Built  up 

Solid  forged 

Thickness  of  crank  web .  .  . 

A=o.6D  too.-j  D 

0.55  Z)  to  0.65  Z) 

Diam.  of  crank  pin 

5  =  1 .  05  Z?  to  i.iD 

I  .  05  Z)  to  I  .  I  Z? 

Length  of  crank  pin 

C=see  main  bearings 

Thickness  of  coupling 

E  =  o.2sD  too.28Z? 

0.  2  Z)  to  0.22  D 

Main  bearing  clearance. . . . 

7^  =  1  to  f  inch 

i  to  1  inch 

Coupling  clearance 

G  =  2  to  3  inches 

2  to  3  inches 

Eccentric  pad  clearance .  .  . 

/7=J  to  i  inch 

i  to  1  inch 

Eccentric  pad  diam 

K  =  D+l  inch 

Z?+f  inch 

Crank  web  holes 

L  =5+iinch 

Crank  web  radius 

l/=o.88L 
iV  =  o.93L 

Crank  web  radius 

Crank  web  width 

0  = 

1.05  5  to  I .  I  B 

Metal  between  holes 

P  =0.45  Z,  at  least 

The  thickness  of  the  crank  webs  is  sometimes  increased  from 
0.6  D  at  the  first  cylinder  to  0.7  Z>  at  the  last. 

The  diameter  of  the  coupling  flange  should  be  about  2  {J  +  d). 
(See  Formula  (24).) 

41.  Lloyd's  Rules  for  Determining  Sizes  of  Shafts  (1915-16). 
—  The  diameters  of  intermediate  (line)  shafts  are  to  be  not  less 
than  those  given  by  the  following  formula: 

For  compound  engines  with  two  cranks  at  right  angles  — 
Diameter  of  intermediate  shaft  in  inches 

=  [0.4  A  +  0.006  D  +  0.02  S]  </P. 
For  triple  expansion  engines  with  three  cranks  at  equal  angles  — 
Diameter  of  intermediate  shaft  in  inches 

=  [0.038  A  +  0.009  B  +  0.002  D  +  0.0165  S]  v^P. 

For  quadruple  expansion  engines  with  four  cranks  — 
Diameter  of  intermediate  shaft  in  inches 
=  [0-033  ^  +  o.oi  B  +  0.004  C  +  0,0013  D  +  0.0155  S]  V  p^ 


DESIGN   OF   ENGINE   PARTS 


47 


A  =  diameter  of  high-pressure  cylinder  in  inches. 
B  =  diameter  of  first  intermediate  cylinder  in  inches. 
C  =  diameter  of  second  intermediate  cyHnder  in  inches. 
D  =  diameter  of  low-pressure  cylinder  in  inches. 
S  =  stroke  of  pistons  in  inches. 

F  =  boiler  pressure  above  atmosphere  in  pounds  per  square 
inch. 

,     ,  koj-^ 

-J 


1" 

1 

*-c 

-^ 

^A-^ 

t 

^  J  1  „ 

_j 

m 



t*ti^ 

l«-t. 

- 

Jf 

I 

v 

V 

I 

Q 

A 

1j 



A 

- 

1 

Up 

Fig.  21. 

The  diameter  of  the  crank  shaft,  and  of  the  thrust  shaft  under 
the  collars,  to  be  at  least  f^th  of  that  of  the  intermediate  shaft. 
The  diameter  of  the  thrust  shaft  may  be  tapered  off  at  each  end 
to  the  same  size  as  that  of  the  intermediate  shaft. 

The  diameter  of  the  screw  shaft  to  be  equal  to  the  diameter  of 

intermediate  shaft  (found  as  above)  multiplied  by  (0.63  +  ^— ^ — 


)■ 


but  in  no  case  to  be  less  than  1.07  T,  where  P  is  the  diameter  of 


48        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

propeller,  and  T  the  diameter  of  intermediate  shaft,  both  in 
inches.  This  size  of  shaft  is  intended  to  apply  to  shafts  fitted 
with  continuous  Uners  the  whole  length  of  the  stern  tube,  as 
provided  for  in  Section  8,  paragraph  3.  If  no  liners  are  used 
or  if  two  separate  liners  are  used,  the  diameter  of  the  shaft 
should  be  |^th  that  given  above. 

The  diameter  of  screw  shaft  is  to  be  tapered  off  at  the  forward 
end  to  the  size  of  the  crank  shaft. 

42.  Internal  Combustion  Engines.  —  Rules  for  Determining 
Sizes  of  Shafts.  The  crank,  intermediate,  and  other  shafts  if 
of  ordinary  mild  steel  are  to  be  of  not  less  diameters  than  as 
given  in  the  following  table. 

For  petrol  or  paraffin  engines  for  smooth  water  services: 

Diameter  of  crank  shaft  in  inches  =  C^D-S, 
where  D  =  diameter  of  cylinder  in  inches, 

S  =  stroke  of  piston  in  inches. 


Four-stroke  cycle 


For  I,  2,  3,  or  4  cylinders. 

For  6  cylinders 

For  8  cylinders 

For  12  cylinders 


Two-stroke  cycle 


I  or  2  cylinders 

3  cylinders 

4  cylinders 
6  cylinders 


Bearing  be- 
tween each 
crank 


C  =  0.34 
C  =  0.36 
C=o.38 
C=o.44 


Two  cranks 

between  the 

bearings 


C=o.38 
C=o.40 
C=o.425 
C=o.49 


For  open  sea  servace  add  0.02  to  C. 

Diameter  of  intermediate  and  screw  shafts  in  inches 


=  C<^D''S  {n  +  3), 
where  D  =  diameter  of  cylinder  in  inches, 

S  =  stroke  of  piston  in  inches, 
n  =  number  of  cylinders. 


For  smooth  water  services 


C=o.  155  for  intermediate  shafts 

C=o.  1 70  for  screw  shafts  fitted  with  continuous  liners. 

C  =  o.  180  for  screw  shafts  fitted  with  separate  liners  or 

with  no  liners 


For  open  sea  services 


C=o.  165 
C  =  o.  180 

C  =  0.  IQO 


DESIGN  OF  ENGINE   PARTS  49 

In  engines  of  two-stroke  cycle  n  is  to  be  taken  as  twice  the 
number  of  cylinders. 

When  ordinary  deep  thrust  collars  are  used  the  diameter  of 
the  shaft  between  the  collars  is  to  be  at  least  .f  o  th  of  that  of  the 
intermediate  shaft.  In  the  cases  of  Diesel  and  other  engines  in 
which  very  high  initial  pressures  are  employed,  particulars  should 
be  submitted  for  special  consideration. 

TORSIONAL   VIBRATION   OF   SHAFTING 

When  the  turning  moment  exerted  upon  a  shaft  varies  in 
intensity  there  will  be  a  certain  amount  of  torsional  vibration 
of  the  shafting.  This  vibration  will  introduce  large  stresses  if 
the  variation  in  the  intensity  of  the  turning  moment  coincides 
with  the  natural  period  of  vibration  of  the  shafting,  or  with  some 
multiple  of  that  period. 

43.  Masses  Affecting  Torsional  Vibration.  —  In  determining 
the  period  of  vibration  of  the  shafting  the  masses  of  the  following 
parts  must  be  used,  —  the  propeller  and  entrained  water,  pro- 
peller shaft,  line  shaft,  thrust  shaft,  crank  shaft,  connecting  rod 
ends,  and  reciprocating  parts.  Approximations  must  be  made 
in  certain  cases.  The  mass  of  the  water  entrained  by  the  pro- 
peller is  assumed  to  be  25  per  cent  of  its  mass.  The  cranks  are 
reduced  to  one  equivalent  crank  at  the  middle  of  the  length  of 
the  crank  shaft.  The  reciprocating  parts  travel  a  distance 
equal  to  twice  the  stroke  for  every  revolution  while  the  crank 
pin  travels  a  distance  of  tt  strokes.  For  this  reason  it  is  usual  to 
assume  that  the  effect  of  the  reciprocating  parts  is  equivalent 

2 
to  that  of  a  single  mass  at  the  crank  pin  equal  to  -  the  mass  of 

TT 

the  reciprocating  parts. 

44.  Equivalent  Masses  at  Crank  Circle.  —  All  of  these  masses 
must  be  reduced  to  equivalent  masses  at  the  crank  circle.  This 
can  be  done  by  finding  the  polar  moment  of  inertia  of  the  parts 
about  the  center  line  of  the  shaft  and  then  placing  at  a  distance  r 
such  masses  as  will  give  the  same  moment  of  inertia. 

Equivalent  masses  at  crank  pin  =  ^p  (    )  — 


50        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

/p  =  polar  moment  of  inertia  (pounds-feet^J . 
r  =  radius  of  crank  pin  circle  in  feet. 

45.  Relation  between  Force  and  Amplitude  of  Vibration.  — 

Let      m  =  mass  of  a  piece  of  shafting  reduced  to  the  crank 
circle. 
K  =  force  at  crank  circle  necessary  to  produce  a  twist 
of  I  inch  arc  measured  at  crank  circle. 

The  time  for  one  complete  vibration  of  such  a  shaft  will  be 

or  K=^m. 

Let  CO  =  —  • 

Then      K  =  w^m  for  i  inch  arc  of  amplitude  on  radius  r. 
sK  =  F  —  soi^m  =  force  for  amplitude  s. 

Tl 

46.  Angle  of  Twist.  —  G  =  —  • 

61  p 

T  =  twisting  moment  (foot  pounds) . 
I  =  length  of  shaft  (feet). 
6  =  angle  of  twist  in  circular  measure. 
Ip  =  polar  moment  of  inertia  of  shaft  (square  inches- 
feet^). 
Then 

Q  =  IL  =  M.  (2  ) 

GIp         Crl  p 

F  =  force  acting  at  radius  r. 

In  the  case  of  a  shaft  twisted  by  the  inertia  of  its  own  mass,  the 
amplitude  of  the  arc  of  torsion  s  varies  as  the  distance  x  from  the 
origin. 

5  =  ex. 

F  =  S(j?m  =  cxoy^m. 

«  =  ^j--  (28) 


DESIGN  OF  ENGINE   PARTS  51 

If  Wi  =  mass  of  shaft  per  unit  length,  the  angle  between  two 
successive  infinitesimal  masses  dx  apart  = 

.        cxoi'mi  dxrx      corr        ,  , 
dd  = — =    —  niix-  dx. 

Clip  Crip 

The  angle  at  the  end  of  the  shaft  at  a  distance  /  from  the  origin: 


cod-r   T'        „  ,        curr  Pnii 
=  — r    /    niiX'  dx  = 


GI p  *Jq  GIp    3 

Since  Inii  =  m, 

then  dm  =  7r~  ~  ^  • 

(^h  3 

From  (28)  a  single  mass  nh  Sit  a  distance  /  from  the  origin  would 
by  its  own  inertia  produce  an  angle  of  twist, 

Gl  p 

Therefore  we  can  substitute  for  the  mass  of  the  shaft  distributed 
over  a  length  /,  a  single  mass  of  one- third  the  mass  of  the  shaft 
at  a  distance  /  from  the  origin. 

47.  Equivalent  Shaft  Length  for  Reduced  Diameter.  —  When 
the  shafts  are  of  different  diameters  they  should  be  reduced  to 
the  diameter  of  the  smallest  shaft,  and  the  length  decreased 
enough  to  make  the  torsional  angle,  for  a  given  twisting  moment, 
the  same  for  the  actual  and  reduced  diameter. 

Let  /  =  length  of  shaft. 

k  =  reduced  length  of  shaft. 
d  =  diameter  of  shaft. 
di  =  diameter  of  smallest  shaft. 

From  Formula  (27),  6  will  remain  constant  if 

48.  Crank-shaft  Mass  and  Propeller  Mass.  —  The  vibrating 
masses  are  reduced  to  two  equivalent  masses,  one  at  the  pro- 
peller and  one  at  the  middle  of  the  crank  shaft.     If  these  two 


52        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

masses  are  vibrating  freely  they  must  have  the  same  period  and 
the  momentum  of  one  mass  must  be  equal  but  opposite  to  the 
momentum  of  the  other.  Between  the  two  masses  will  be  a  node 
where  the  shaft  will  have  no  torsional  vibration.  This  node  will 
be  at  the  center  of  graxdty  of  the  system. 

Let    Ml  =  mass  at  propeller. 

M2  =  mass  at  middle  of  crank  shaft. 
Li  =  distance  of  Mi  from  node. 
L2  =  distance  of  Mo  from  node. 
Si  =  ampKtude  of  \ibration  of  Mi. 
S2  =  amplitude  of  \dbration  of  M2. 
Momentum  of  Mi  =  MiSi  =  MiCLi. 
Momentum  of  M2  =  M2S2  =  M2CL2. 
MiCLi  =  M2CL2. 

"     Mo      Li 

or  the  node  is  at  the  center  of  gravity  of  the  system. 

The  propeller  mass  will  be  made  up  of  the  masses  of  the  pro- 
peller, entrained  water,  and  the  portion  - — ^—y-  of  the  shafting 

Li  +  Lo 

mass.     The  crank-shaft  mass  will  be  made  up  of  the  masses  of 

the  cranks,  reciprocating  parts,  and  the  portion  - — ■ — —  of  the 

L\  -\-  L2 

shafting  mass. 

49.   Rate  of  Vibration.  —  From  Formula  (27), 


If 
and 


From  Formula  (26),  t  =  2  it  Vt^T"  ~  ^  irr\l  -^' 

'    (jlp  Lrip 


e 

-GU    '"^''^ 

Trl 
Gh 

dr 

=  i"    then  T  -- 

=  Kr 

KrH 
GIp 

=  I. 

:.K 

GIp 

rH 

DESIGN  OF   ENGINE   PARTS  53 

The  number  of  oscillations  per  minute  will  be 

(30) 


t  nrV       ' 


/        -ky  '    ml 

Y  =  radius  of  crank  circle  in  feet. 
G  =  12,000,000  for  ordinary  steel. 
Ip  =  polar  moment  of  inertia  (square  inches-feet^) . 
fn  =  mass  of  \ibrating  parts. 

I  =  distance  from  \ibrating  mass  to  node  (feet). 

Since  MiLi  =  M-iLi  we  can  use  either  the  propeller  mass  and 
its  distance  from  the  node,  or  the  crank-shaft  mass  and  its  dis- 
tance, n  is  called  the  critical  number  of  revolutions  for  that 
engine  and  it  is  desirable  that  n  should  not  equal  the  normal 
r.p.m.  of  the  engine  or  any  multiple  of  the  r.p.m. 

PISTON   RODS 

50.  Load  upon  Piston  Rod.  —  The  piston  rod  is  a  cylindrical 
column  with  the  ends  shaped  as  in  Plates  1,2,  and  3.  The  middle 
portion  carries  an  alternating  load  but  the  ends  are  so  con- 
structed, with  shoulders  and  tapered  parts,  that  the  threaded 
part  carries  only  an  intermittent  load.  The  diameter  of  the 
middle  portion  of  the  rod  is  calculated  by  means  of  the  Column 
Formula  (12),  while  the  ends  are  figured  for  tension  only.  The 
rod  should  be  figured  for  the  maximum  load  to  which  it  will  be 
subjected,  and  this  load  will  be 

^^^.Xl.H.P.^X.»,ooo.  (^^^ 

I.H.P.  =  the   maximum    indicated    horse-power   in    a   single 
cylinder. 
P.S.  =  piston  speed  of  engine  in  feet  per  minute. 

51.  Diameter  of  Piston  Rod.  —  The  piston  rod  should  be 
treated  as  a  column  with  free  ends  whose  length  is  equal  to  the 
distance  from  the  under  side  of  the  piston  to  the  center  line  of  the 
crosshead  pins.     This  length  will  be  appro.ximately 

I  =  S  -\-  Hd  +  6",  merchant  engines 
=  S  -\-  Hd  -\-  3",  naval  engines. 


54       THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILL\RIES 

5  =  Stroke  of  engine  in  inches. 
Hd  =  diameter  of  H.P.  cylinder  in  inches. 

If  the  cylinder  bottom  is  deeper  than  1.4  X  diameter  of  the 
piston  rod,  the  assumed  length  should  be  increased.  The 
diameter  of  column  given  by  Formula  (12)  should  be  increased 
by  \  inch  to  allow  for  turning  the  rod  down  when  it  wears  un- 
evenly. The  working  stress  factor  to  be  used  in  the  formula 
shoiild  be  18  for  merchant  engines  but  can  be  reduced  to  12  for 
torpedo  boat  engines.  Hollow  piston  rods  are  used  upon  naval 
engines  and  some  yacht  engines  where  it  is  desirable  to  save 
weight.  The  diameter  of  the  hole  in  the  rod  is  usually  from  40 
to  65  per  cent  of  the  outside  diameter  of  the  rod.  The  ultimate 
strength  of  the  steel  used  for  the  rods  of  merchant  engines  varies 
from  60,000  pounds  to  80,000  pounds  per  square  inch,  while  for 
naval  engines  it  is  often  as  high  as  95,000  pounds. 

52.  Piston-rod  Ends.  —  The  shoulders  at  the  ends  of  the  rod 
can  be  negative  as  shown  on  Plate  3,  or  positive,  see  Plate  2. 
Negative  shoulders  are  usually  made  not  less  than  |  inch  in 
width,  while  positive  shoulders  are  seldom  less  than  \  inch  wide. 
The  taper  should  be  from  2^  inches  per  foot  to  3  inches  per  foot; 
if  it  is  made  much  finer  than  that  it  will  be  difficult  to  remove 
the  parts.  In  some  cases  the  taper  is  omitted,  see  Plate  i.  If 
the  threaded  end  is  3  inches  or  more  in  diameter  the  area  at  the 
root  of  the  thread  can  be  calculated  to  carry  the  load  with  a 
working  stress  factor  of  10.  The  number  of  threads  per  inch  is 
usually  4,  therefore  the  diameter  at  the  root  of  the  thread  must 
be  increased  by  1.299  -^  4  =  0.325  i^ch  to  allow  for  cutting 
the  threads. 

The  approximate  diameter  of  the  rod  can  be  found  from  the 
curves  in  Fig.  22  by  adding  \  inch  to  the  diameters  there  given 
for  different  relations  of  load  and  length.  The  curves  are  con- 
structed for  steel  of  80,000  pounds  ultimate  strength  and  for  a 
working  stress  of  4450  pounds.  For  steel  of  any  other  ultimate 
strength  the  diameter  mil  vary  roughly  as  the  fourth  root  of  the 
ratio  of  that  ultimate  strength  to  80,000  pounds.  When  hollow 
rods  are  used  the  diameter  will  have  to  be  increased  about  10 


DESIGN   OF   ENGINE   PARTS 


55 


per  cent  when  the  diameter  of  the  hole  is  about  0.6  the  diameter 
of  the  rod. 


12 

Column  Sizes 

: 

I'll                II 
Jltimate  Strength  =  80,000  Lbs. 

^ 

•^ 

.-- 

"^ 

11 

c 

/VorJing  Stress=4,450  Lbs. 

.„.\,62>-' 

-^ 

.^ 

^^ 

^-^ 

^ 

iJOLL"     ""     "          "^ ~ 

MM  tND 

b  AK 

^ 

^ 

^ 

10 

■ 

J££ 

. 

^ 

^5&^ 

-^ 

, — 1 

'^ 

-^ 

"^ 

: 



--- 

^^ 

--^'^ 

^^ 

-^ 

^ 

9 

^ 

-^r^ 

.^ 

Jo°2^ 

^^ 

---1 

-^ 

^ 

: 

^ 

^^ 

-^ 

,0^ 

--^J'^l^^ 

^' 

^  .^ 

^ 

:^ 

y  8 

; 

^ 

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^ 

r::^ 

;^ 

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L4ss^ 

^^^ 

b 

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: 

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^^1^ 

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222--' 

^^^ 

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02^^ 

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^-""^ 

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cr 

u 

f — 

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^ 

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OU,.*' 

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r 

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JOJO. 

1  r  M 

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,,-, 

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T^r^ 

111. 

1 1 1 

n  1  , 

.III 

■  1  1  1 

,,,, 

111' 

Length  of  Column,  in  Inches 
Fig.  22. 


CROSSHEADS   AND    SLIPPERS 

53.  Types  of  Crosshead.  —  It  is  the  function  of  the  crosshead 
to  make  the  connection  between  the  piston  rod  and  the  connect- 
ing rod.     The  connection  can  be  made  in  three  ways:    (i)  by 


56       THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

means  of  a  block  with  two  pins  which  bear  in  boxes  in  the  con- 
necting rod  fork,  see  Fig.  23;  (2)  by  means  of  a  single  pin  held 
by  the  crosshead  jaws  bearing  in  a  box  in  the  connecting  rod,  see 


Fig.  23. 


kU 


■^ ^ 


HJ 


Fig.  24. 


Fig.  24;  (3)  by  means  of  a  box  on  the  end  of  the  piston  rod 
which  provides  bearing  for  a  pin  held  by  the  fork  of  the  connect- 
ing rod,  see  Fig.  25.  The  first  is  the  most  common  type  and  is 
found  in  both  merchant  engines  and  naval  engines;   the  second 


DESIGN   OF  ENGINE   PARTS 


57 


type  is  used  on  boats  running  on  the  Great  Lakes;  and  the  third 
type  is  used  mainly  in  light  high-speed  engines  such  as  those  for 
yachts. 


Fig.  25. 


54.  Size  of  Crosshead  Pins.  —  The  size  of  the  crosshead  pin 
is  determined  by  the  amount  of  bearing  surface  needed  to  keep 
the  unit  bearing  pressure  between  850  pounds  and  1200  pounds 
for  merchant  engines  and  between  1200  pounds  and  1800  pounds 
for  naval  engines.  The  bearing  surface  is  taken  as  the  projected 
surface  of  the  pin  and  is  equal  to  the  length  X  diameter.  The 
diameter  of  the  pin  or  pins  is  usually  from  i.i5Z)toi.25Z>,  and 
the  length  is  such  as  to  give  the  necessary  surface.  The  pin  is 
usually  made  from  |  to  j  inch  longer  than  necessary  for  surface 
alone  to  allow  for  clearances.     (For  D,  see  Fig.  23.) 

55.  Size  of  Crosshead  Block.  —  The  crosshead  block  with 
projecting  pins  must  be  figured  for  splitting  on  a  plane  through 
the  center  line  of  the  piston  rod.  It  is  usual  to  figure  the  block 
as  though  it  were  a  beam  supported  at  the  mid-length  of  the  pins 
and  loaded  at  the  middle  of  the  block  with  a  load  equal  to  W, 
the  piston  rod  load.  The  block  is  approximately  a  cube  and  the 
breadth  and  depth  can  be  assumed  and  only  the  height  needs  to 
be  figured.  The  breadth  F,  see  Fig.  26,  will  be  from  1.5  Z)  to 
i.y  D.  The  block  is  made  of  forged  steel  or  cast  steel  and  since 
the  load  is  alternating  a  working  stress  factor  of  1 2  must  be  used. 


58        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


If  we  treat  the  block  and  pins  as  a  beam  supported  at  mid- 
length  of  the  pins  the  length  of  the  beam  will  be 

I  ^  F  +  J 

and  the  height  of  the  block,  E,  can  be  found  from  a  formula 

derived  from  the  ordinary  beam 
formula : 


c 


k- 


w 

2 


-+-J-H 


_  J?>  wi 

V     2bf 


(32) 


l-'.-i-l 


6  k 


± 

I 

.1^ 


w 
2 


b  =  net  breadth  of  section 
=  F  —  mean  diam- 
eter of  hole  through 
block. 

/  =  working  stress. 
W  =  maximum  load. 

I  ^   F  -\-  J  (see  Fig.  26). 

Let  the  depth  of  the  block,  G,  equal  the  height,  E. 

56.  Types  of  Slippers.  —  The  slippers  attached  to  the  cross- 
head  blocks  are  of  four  different  types:  (i)  the  box  slipper,  see 
Fig.    27;    (2)  the  single  slipper,   see  Fig.    23;     (3)  the  double 


A 
Fig.  26. 


—  A- 


■^ 


}f^M 


Solid 


Fig.  27. 

slipper,  see  Fig.  28;  (4)  the  four-slipper  type,  see  Fig.  29.  The 
box  slipper  is  used  mainly  upon  engines  of  1000  I.H.P.  or  less, 
and  also  upon  engines  which  are  run  "backing"  as  much  as 
"ahead,"  such  as  ferry-boat  engines.     The  single  slipper  is  the 


DESIGN  OF   ENGINE   PARTS 


59 


most  used  and  is  found  upon  engines  of  all  sizes,  both  merchant 
and  naval.  The  double  slipper  is  not  used  to  any  great  extent 
since  it  requires  heavy  columns  upon  the  front  of  the  engine  as 
well  as  upon  the  back  to  carry  the  backing  guides.     The  four- 


;ik 

rz 

1 

-A 

-^t^. 

/ 

-//^\ 

t 

A 

^zz'i 

-I 

O 

V 

-u- 

± 

z 

/ 

--->    ( — T^- 

I  P— Bolt 

P= 

^T^ 1 

Fig.  29. 

slipper  t}'pe  is  used  upon  large  engines  where  the  great  weight 
of  the  cylinders  makes  it  advisable  to  use  four  supports  rather 
than  two.  These  four  supports  can  be  made  to  carry  the  four 
guide  surfaces. 


6o       THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

57.  Size  of  Slipper.  —  The  load  upon  the  slipper  is  zero  at 
the  beginning  and  end  of  the  stroke  and  a  maximum  at  mid- 
stroke.     This  maximum  load  will  be 


G'  =  tFtansin-i^, 

V 


but  it  is  usual  to  assume  it  to  be 


G  =  W 


(33) 


The  surface  of  the  slipper  should  be  such  that  the  pressure 
per  square  inch  is  from  55  to  65  pounds  for  merchant  engines, 
and  from  75  to  100  pounds  for  naval  engines.  In  all  t^^Des  ex- 
cept the  single-slipper  type  the  "backing"  surface  is  equal  to  the 
"ahead"  surface.  The  breadth  of  the  slipper  is  usually  from 
2.5  to  3  times  the  diameter  of  the  piston  rod.  In  the  single- 
slipper  t>^e  the  connection  between  the  block  and  the  slipper  is 
made  by  means  of  a  web  which  must  be  thick  enough  to  be  rigid. 
The  thickness  of  this  web  is  usually  about  0.5  the  diameter  of 
the  piston  rod,  and  the  minimum  breadth  of  the  space  on  the 
back  of  the  sHpper  occupied  by  the  web  and  its  hllets  will  be 
about  3  inches.  In  order  that  the  backing  surface  shall  not  be 
less  than  75  per  cent  of  the  ahead  surface  the  minimum  breadth 
of  the  single  slipper  will  be  12  inches.     The  ratio  between  the 

length  and   breadth    of   the 
^     ^j     \      J      slipper  will  vary  from  i  in 
JLj— T--i;0      small  engines  to  2  in  large 
engines. 

58.  Thickness  of  Slipper. 
—  The  ahead  and  backing 
surfaces  are  usually  lined 
■with  white  metal  of  a  total 
thickness  of  |  inch.  The 
white  metal  is  held  in  dovetailed  grooves  about  |  inch  deep  so 
that  the  surface  of  the  white  metal  projects  I  inch  beyond  the 
body  of  the  slipper  and  that  amount  of  wear  can  take  place  be- 
fore the  steel  of  the  shpper  will  touch  the  guide  surface.  The 
slipper  is  usually  made  separate  from  the  crosshead  block  and 


DESIGN  OF   ENGINE   PARTS  6 1 

is  attached  to  it  by  means  of  four  or  more  bolts  which  must  be 
large  enough  in  the  case  of  the  box  and  single  slipper  to  carry 
the  load  when  backing.  The  slipper  can  be  made  of  cast  steel 
or  forged  steel,  and  in  the  case  of  the  single-slipper  type  should 
be  figured  for  bending  at  aa,  see  Fig.  30.  It  is  assumed  that  the 
load  is  acting  at  the  middle  of  the  breadth  of  the  backing  surface 

so  that  the  bending  moment  coming  upon  metal  is  -  X  - .     The 

2       2 

thickness  of  metal  between  the  backs  of  the  white  metal  in  the 

single-slipper  type  should  be 


t  =  \/^-^-  (34) 

K  =  length  of  slipper. 

/  should  be  5000  for  forged  steel  (merchant  engines) . 

8000  for  forged  steel  (naval  engines). 

3500  for  cast  steel. 

The  total  thickness  of  the  slipper  including  white  metal  will  be 
t  +  one  inch. 

59.  Backing  Guide.  —  The  backing  guide  can  be  figured  by 
formula  (34)  if  we  assume  that  only  that  portion  of  the  guide 
in  contact  with  the  slipper  resists  the  backing  load.  The  only 
change  that  will  have  to  be  made  will  be  in  the  value  of  /.  The 
backing  guide  is  almost  always  made  of  cast  iron  since  cast  iron 
and  white  metal  work  well  together.  The  value  of  /  should  be 
1500  for  the  backing  guide  and  the  thickness  obtained  from  the 
formula  will  be  the  thickness  at  dd.  The  guide  can  be  tapered 
down  to  a  thickness  of  i  inch  or  f  inch  at  the  inner  end. 

60.  Backing-guide  Bolts.  —  The  backing  guide  bolts  will 
carry  a  load  greater  than  G,  due  to  the  leverage  which  the  guides 
exert  upon  those  bolts.  The  load  upon  the  bolts  of  one  guide 
will  be 

s  =  GSiA^.  (35) 

e  and  g  have  the  values  shown  in  Fig.  30.  The  clearance 
between  the  body  of  the  bolt  and  the  edge  of  the  slipper  should 


62        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILL\RIES 

be  about  |  inch  and  the  thickness  of  metal  outside  of  the  bolts 
should  be  about  equal  to  the  diameter  of  the  bolts,  Q.  The  lip 
usually  projects  about  f  inch.  The  value  of  e  and  g  will  be  as 
follows : 

e  =  -  +  -    +-• 

2         2  2 

4 

(>  -i-  p 

Assume  for  the  first  trial  that =  2.25  and  determine  the 

S 
size  of  bolts  upon  the  assumption  that  three  bolts  will  carry  the 

load  upon  one  guide.     If  the  diameter  so  determined  gives  a 

g  -f-  p 
value  of equal  to  2.25  approximately,  that  diameter  can 

be  used;  if  the  value  is  considerably  greater,  or  less,  than  2.25,  a 
larger  or  smaller  diameter  must  be  used.  The  bolts  are  usually 
spaced  about  6  diameters  apart  and  have  cylindrical  heads  flush 
^^dth  the  outside  of  the  guide. 

61.  Attachment  of  Slipper.  —  In  the  case  of  the  two- slipper 
and  four-slipper  types  the  slippers  can  be  attached  to  the  cross- 
heads  with  smaller  bolts  than  in  the  case  of  the  single-slipper 
t}^e,  since  in  the  former  cases  the  bolts  do  not  have  to  carry 
the  load  when  backing.  These  bolts  are  usually  made  from  i 
to  ij  inches  in  diameter.  It  will  be  noticed  in  these  two  cases 
that  a  much  stififer  connection  between  the  slipper  and  block 
is  possible  and  that  the  connecting  web  need  be  only  i  inch 
thick. 

Removable  keys  are  usually  provided  on  the  upper  side  of  the 
slippers  so  that  they  can  be  taken  off  without  disturbing  the 
alignment  of  the  rod. 

CONNECTING  RODS 

62.  Types  of  Connecting  Rods.  —  Connecting  rods  are  of  two 
general  types,  the  forked  marine  type  and  the  straight  land  type. 
The  latter  t>^e  of  rod,  see  Fig.  31,  is  used  upon  some  ships  on 


DESIGN   OF   ENGINE    PARTS 


63 


the  Great  Lakes  but  the  forked  t>'pe  is  the  most  common  else- 
where. The  forked  type  of  rod  can  be  divided  into  two  classes: 
(i)  in  which  the  fork  carries  boxes  for  the  crosshead  pins,  see 
Fig.  32;  (2)  in  which  the  fork  carries  the  pin,  see  Fig.  33.  The 
latter  is  used  sometimes  in  naval  engines  and  yacht  engines 
where  weight  is  to  be  saved. 


Fig.  3] 


63.  Diameter  of  Connecting  Rod.  —  The  connecting  rod 
should  be  figured  as  a  column  and  Formula  (12)  can  be  used  for 
finding  the  diameter,  //,  at  the  middle  of  its  length.     The  length 

of  the  connecting  rod  is  usually  between  4  r  and  5  r;   i.e.,  -  =  4 

r 

to  5.     The  usual  ratio  is  4.5  but  in  naval  engines  where  height 

is  of  importance  a  ratio  of  4  is  used. 

The  connecting  rod  and  the  piston  rod  are  usually  made  of  the 

same  quality  of  steel,  and  the  same  working  stress  factor  should 

be  used,  namely  18.     The  maximum  load  to  which  the  rod  is 

subjected  is  somewhat  larger  than  that  for  the  piston  rod,  due 

to  the  fact  that  the  connecting  rod  makes  an  angle  with  the  line 


&4        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


Fig.  32. 


DESIGN   OF   ENGINE    PARTS 


6;; 


of  centers  when  the  maximum  load  occurs.     The  effect  of  this 
angularity  is  to  increase  the  load  W  to  the  following  extent: 
F  =  Wk. 
I 


If 


=    4 


4-25 


4-5 


4-75 


k  =     1.033         I -03           1.026       1.023  1. 02 1 
W  =  maximum  load  upon  piston  rod. 

The  diameter  of  the  rod  at  mid-length  can  be  determined 
approximately  from  the  curves  of  Fig.  22. 


Fig.  33- 


64.  Taper  of  Body  of  Rod.  —  The  accelerating  forces,  which 
are  acting  upon  the  connecting  rod  as  it  swings  back  and  forth 
across  the  line  of  centers,  give  rise  to  a  certain  amount  of  bending. 
This  bending  is  a  maximum  when  the  rod  makes  its  maximum 
angle  with  the  line  of  centers.  The  resultant  of  the  accelerating 
forces  is  acting  at  the  center  of  percussion,  which,  in  a  marine 
cormecting  rod,  is  very  close  to  the  crank  pin.  This  subjects 
the  lower  part  of  the  rod  to  bending.  There  is  also  a  small 
amount  of  bending  introduced  at  this  point  by  the  friction  of  the 
crank  pin  in  the  box.  The  additional  stress  in  the  lower  part 
of  the  rod  due  to  this  bending  is  seldom  figured  but  the  diameter 
of  the  rod  at  the  lower  end  is  arbitrarily  increased.     The  upper 


66        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

end  of  the  rod  can  be  decreased  in  diameter,  since  the  added 
stress  due  to  cokimn  action  is  less  than  at  mid-length  and  very 
little  of  the  cross-bending  is  felt  here.  It  is  usual  to  increase  the 
diameter  at  the  lower  end  of  the  rod  to  i.i  H  and  to  make  the 
diameter  at  the  upper  end  0.9  H^  with  a  uniform  taper  from  one 
point  to  the  other. 

65.  Connecting-rod  Bolts.  —  In  a  rod  of  the  type  shown  in 
Fig.  32  the  bolts  at  either  end  have  to  carry  the  maximum  load 
of  the  rod.  At  the  crosshead  end  there  are  four  bolts  while  at 
the  crank-pin  end  there  are  two.  The  sizes  can  be  determined 
from  the  table  of  bolts,  see  Table  5.  It  is  safer  to  assume  that 
the  load  at  the  crosshead  end  will  be  carried  by  only  three  bolts. 
These  bolts  are  made  with  cylindrical  heads. 

66.  Connecting-rod  Boxes.  —  The  diameter  and  length  of  the 
boxes  at  the  crosshead  and  at  the  crank  pin  must  be  made  to 
suit  the  pins  working  in  them.  The  lugs  on  the  connecting  rod 
to  which  these  boxes  are  attached  have  a  breadth  which  is  less 
than  the  length  of  the  boxes,  so  that  the  boxes  have  a  certain 
amount  of  overhang.  The  breadth  of  the  lugs,  see  Fig.  32,  is 
0.7  of  the  length  of  the  box  at  the  crank-pin,  and  about  0.8  at 
the  crosshead  end.  The  length  of  the  lugs  must  be  sufficient 
to  cause  them  to  project  far  enough  to  accommodate  the  heads 
and  nuts  of  the  bolts.  These  heads  and  nuts  can  cut  into  the 
fillets  but  must  clear  the  body  of  the  rod.  The  thickness  of  the 
lugs  must  be  slightly  greater  than  the  diameter  of  the  bolts 
passing  through  them.  The  clearance  between  the  body  of  the 
bolts  and  the  pins  should  be  about  \  inch  at  the  crosshead  end 
arid  about  ^  inch  at  the  crank-pin  end.  The  distance  between 
center  lines  of  bolts  at  the  crosshead  end  must  be  such  that  the 
body  of  the  bolts  clear  the  crosshead  pins  by  the  proper  amount 
and  the  heads  of  the  bolts  clear  the  fork. 

67.  Connecting-rod  Fork.  —  The  thickness,  Z,  of  the  fork  of 
the  rod.  Fig.  32,  must  be  at  least  equal  to  the  diameter  of  the 
rod  at  the  upper  end  and  is  often  made  from  i  to  j  inch  thicker, 
if  it  does  not  make  the  clearance  between  the  body  of  the  bolts 
and  the  crosshead  pins  greater  than  is  desirable.  In  figuring 
the  fork  it  is  safer  to  assume  the  minimum  thickness.     While 


DESIGN  OF   ENGINE   PARTS 


67 


the  thickness  of  the  fork  is  kept  constant  the  breadth  of  any 
section  must  be  determined  from  the  bending  and  direct  com- 
pression to  which  it  is  subjected.  The  total  stress  upon  any 
section  will  be  the  resultant  of  the  stresses  due  to  direct  com- 
pression, shear,  and  bending.  We  can  take  these  into  account 
by  means  of  the  approximate  formula 


/  = 


h 


+ 


6  PI 


P_ 

2  bh 

P 

4bf 

h  =  breadth  of  fork  sec- 
tion corresponding 
to  distance  /. 
P  =  maximum  load  on 

connecting  rod. 
b  =  thickness  of  fork. 
/  =  distance  from  neu- 
tral axis  of  section 
to  line  of  action  of 
force. 
/  =  stress.     Use  work- 
ing stress  factor  of 
12. 


Let  /  have  successive 
values  such  as  i  inch,  2 
inches,  3  inches,  etc.,  as 
shown  in  Fig.  34,  and 
find  the  values  of  h.  The 
contour  of  the  inside  of  '  ^'^' 

the  fork  is  made  semicircular  and  the  values  of  h  are  to  be 
laid  off  about  normal  to  the  semicircle  so  that  the  center  of 
the  breadth  h  is  the  proper  distance  from  the  line  of  action  of 
the  force.  The  outside  contour  of  the  fork  should  consist 
of  arcs  of  circles,  for  convenience  in  laying  off.  Usually 
two  arcs  of  the  same  radius  can  be  made  to  coincide  closely 
with  the  points.     Forks  are  sometimes  made  with  the  outside 


68        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

contour  a  straight  line;  this  makes  the  fork  heavier  as  the 
straight  line  must  include  the  extreme  point.  The  lowest  point 
of  the  inside  of  the  fork  should  clear  the  end  of  the  piston  rod 
by  about  the  thickness  of  the  nut  on  the  end  of  the  rod.  A 
working  stress  factor  of  12  should  be  used. 

68.  Connecting-rod  Caps.  —  The  caps  of  the  boxes  should  be 
figured  as  beams  with  a  length  equal  to  the  distance  between 
bolt  centers  and  a  breadth  equal  to  the  breadth  of  the  lugs.  The 
conditions  of  loading  and  support  are  such  that  the  beam  does 
not  fall  into  any  one  of  the  usual  classes;  the  load  is  partially 
distributed  and  the  condition  of  the  ends  is  somewhere  between 
that  of  being  fixed  and  being  supported.     A  bending  moment 

of  —  will  be  a  close  enough  approximation.     Since  the  section 
6 

of  the  beam  is  rectangular  the  height  of  it  will  be  given  by  the 
following  fonnula: 


PI 

Crosshead  end  S  =  \^ ~t-.-  (37) 

^  2hJ 


PI 
Crank-pin  end  S  =  \  —  •  (38) 

P  =  maximum  load  in  the  connecting  rod. 
I  =  distance  between  bolt  centers. 
h  =  breadth  of  cap. 
/  =  allowable  stress. 

The  load  upon  the  caps  is  intermittent  and  the  lowest  working 
stress  factor  would  be  8,  but  for  the  sake  of  stiffness  it  should  be 
10.  The  caps  are  made  of  bronze,  cast  steel,  and  wrought  steel, 
the  latter  being  the  most  common.  When  the  cap  and  brass  are 
all  in  one  piece  the  cap  should  have  the  required  thickness  ex- 
clusive of  the  white  metal. 

69.  Connecting-rod  Brasses.  —  The  brasses  are  shells  carry- 
ing the  white  metal  for  the  pins  and  enclosing  the  bolts.  The 
thickness  of  metal  around  the  bolts  is  about  one-fourth  the 
diameter  of  the  bolt,  and  the  total  thickness  of  the  white  metal 
is  from  ^  to  f  inch.  The  two  brasses  are  separated  by  a  thick 
cast  iron  liner  of  horseshoe  shape,  from  i  to  if  inches  thick,  and 


DESIGN   OF   ENGINE   PARTS 


69 


also  by  several  tin  liners  whose  thickness  varies  from  g\  to  i 
inch.  The  least  thickness  of  the  brasses  should  be  about  0.2  X 
diameter  of  pin.  The  distance  from  the  center  of  the  pin  to  the 
back  of  the  brasses  should  be  two-thirds  the  diameter  of  the  pin. 


PISTONS 


70.   Types  of  Pistons.  —  There  are  two  types  of  pistons  in 
general  use,  the  conical,  cast-steel  type,  see  Fig.  35,  and  the  hol- 


FiG.  35 

low,  cast-iron,  box  t}^e,  see  Plates  i,  2,  and  3.  The  cast-steel 
piston  is  lighter  and  stiffer  than  the  cast-iron,  and  is  used  where 
weight  must  be  saved,  and  where  the  engine  makes  a  high  num- 
ber of  revolutions  per  minute.  The  cast-iron  piston  gives  a 
cylinder  of  simpler  construction,  but  the  piston  cannot  be  run 
much  over  100  r.p.m. 
71.   Cast-iron  Piston. 

Depth  of  piston  at  center     =  1.5  (/. 
Depth  of  piston  at  rim         =  1.2  d. 
Thickness  of  face  and  back  of  piston  =  i  inch. 
Thickness  of  metal  around  piston  rod  =  0.5  (/. 

d  =  diameter  of  piston  rod. 
Pitch  of  follower  studs         =  6  diameters  on  H.P. 

=  7  diameters  on  j\I.P. 
=  8  diameters  on  L.P, 
Thickness  of  ribs  of  piston  =  |  inch. 


70       THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


72.    Cast  steel  Pistons. 
Depth  of  boss  at  center    =  k  =  d  (naval  engines). 
Depth  of  boss  at  center    =  k  —  1.2  d    to    i.^d    (merchant    en- 
gines). 

Thickness  of  metal  around  piston  rod  =  n  =  0.4  d. 


200 
=  m  =  0.4  /. 


Thickness  of  piston  metal  at  center    =  /  = v  p  +0.5  inch. 

200 

Thickness  of  piston  metal  at  rim 

d  =  diameter  of  piston  rod. 

D  =  diameter  of  cylinder. 
P  may  be  taken  as  follows: 


Triple 


Quadruple 


H.P.  cylinder,  0.5  boiler  pressure.  .  . 

1  M.P.  cylinder,  0.25  boiler  pressure. 

2  M.P.  cylinder 

L.P.  cylinder,  0.20  boiler  pressure. .  . 


0.45  boiler  pressure 
o .  20  boiler  pressure 
o.  175  boiler  pressure 
o.  10    boiler  pressure 


6^"  Co'-e sj 


(Mai  l^\ 


4-Links  per  boat 
Class  A-S.F. 


l{"  Brass 
Machine  Screws 


Fig.  36. 


DESIGN  OF  ENGINE   PARTS 


71 


The  over-all  height  of  cast-steel  pistons  is  usually  made  the 
same  for  all  cylinders,  and  the  details  of  the  boss  and  of  the  rims 
are  usually  the  same  for  all.  The  pistons  will  have  a  different 
slope  in  each  cylinder,  but  in  the  L.P.  this  slope  on  the  under 
side  should  not  be  less  than  i  in  6  for  engines  using  steam  of  175 
pounds  pressure,  and  not  less  than  i  in  3  if  the  steam  pressure  is 
300  pounds. 

73.  Piston  Rings.  —  The  piston  rings  are  made  of  cast  iron 
and  are  usually  of  the  restrained  type,  as  shown  in  Fig.  36.     The 


D      A     B 

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\%- 

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2%' 

Ws 

V 

%• 

\H' 

OVER 

70' 

m 

IVi^Wf 

r 

V 

Wx 

Fig.  37. 


D      A     B     C     E  1  F     G 

H  1  J 

48-  jlJ-r 

IJ^' 

3" 

Wi'l  V 

2H- 

Ws 

%■ 

60- 

\H- 

m- 

3" 

m 

r 

IVi 

\]^' 

H- 

72" 

\H- 

]]4- 

3H- 

\%-\\}i- 

2%- 

m- 

H- 

04" 

\%- 

\H' 

3H- 

15^1^' 

2%' 

\H- 

%• 

96"    \yi\\\A 

^2\m'\i4- 

2H' 

nr 

%• 

Fig.  38. 

rings  are  cast  solid  and  larger  in  diameter  than  the  cylinder  they 
are  to  fit.  A  lug  is  cast  upon  the  inside  of  the  ring  and  at  this 
place  a  piece  of  the  ring  is  cut  out.  The  ring  is  then  sprung 
together,  held  by  a  strap  or  bolt  at  the  lug.  and  turned  to  fit  the 
cylinder.     As  the  ring  wears  it  is  let  out  enough  to  take  up  the 


72        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

wear  but  not  enough  to  press  unduly  upon  the  liner  or  barrel. 
With  unrestrained  rings  the  steam  works  in  back  of  the  rings 
and  forces  them  out  upon  the  liner  causing  a  large  loss  in  friction. 

74.  Piston  Rims.  —  Some  details  of  piston  rims  are  shown 
in  Figs.  37  and  38,  and  the  proper  proportions  for  certain  sizes 
of  L.P.  cylinders  are  given  in  the  accompanying  tables. 

CYLINDERS   AND   COVERS 

75.  Cylinder  Castings.  —  CyKnders  are  usually  cast  with  the 
barrel,  bottom,  and  valve  chest,  in  one  piece.  Occasionally  the 
valve  chest  is  a  separate  casting  bolted  to  the  cylinder,  and  in 
the  case  of  some  torpedo  boat  engines  the  cylinder  bottom  is 
bolted  on,  but  this  latter  construction  is  unusual.  The  cylinder 
casting  is  quite  compHcated  and  for  this  reason  it  is  desirable  to 
use  a  soft  grade  of  cast  iron  which  will  run  easily  and  make  a 
good  casting.  A  soft  grade  of  cast  iron,  however,  does  not  de- 
velop a  good  wearing  surface  for  the  piston  rings,  and  for  this 
reason  liners  made  of  a  hard-grained  iron  are  often  used.  If  a 
cylinder  is  to  be  jacketed  with  steam  there  must  be  a  liner,  but, 
for  the  reason  given  above,  liners  are  often  used  when  no  jacket 
steam  is  to  be  employed.  Even  if  the  space  between  the  liner 
and  the  barrel  is  not  to  be  used  for  jacketing  it  is  generally  con- 
nected to  the  steam  line  and  used  for  warming  up  the  engine  after 
it  has  been  shut  down  for  any  length  of  time. 

76.  Cylinder  Ends.  —  The  cylinder  ends  are  sometimes 
jacketed,  in  which  case  the  cylinder  bottom  and  cylinder  cover 
are  made  double,  with  the  two  walls  stiffened  by  occasional 
ribs.  If  the  ends  are  not  to  be  jacketed  they  can  be  made  with 
a  single  wall  stiffened  by  deep  ribs.  The  cover  and  bottom  are 
occasionally  made  double  merely  for  the  sake  of  stiffness. 

77.  Sizes  of  Parts.  —  The  thickness  of  the  liner  and  of  the 
barrel  can  be  computed  by  means  of  the  formula  given  below: 

^^(P  +  25)D      ,^^. 

6000  100  +  Z)  ^^^^ 

t  =  thickness  of  liner. 
P  =  maximum  pressure  in  cylinder. 
D  —  diameter  of  cylinder  in  inches. 


DESIGN  OF   ENGINE   PARTS  73 

The  value  of  P  can  be  taken  as  follows: 

Triple   and   Quad.   H. P.  cylinder  P  =  boiler      pressure     (gage). 

Triple M.P.  cylinder  ^  =  0.5  boiler  pressure  (gage) 

Triple L.P.  cylinder  P  =  0.375  boiler pressure(gage). 

Quadruple I. M.P.  cylinder  P=o.6  boiler  pressure  (gage). 

Quadruple 2  M.P.  cylinder  P  =  o.4  boiler  pressure  (gage). 

Quadruple L.P.  cylinder  ^  =  0.25  boiler  pressure  (gage). 

It  is  customary  to  make  the  liners  of  all  cyhnders  of  the  same 
thickness  and  as  the  liner  for  the  H.P.  cylinder  usually  figures 
out  to  be  the  largest  it  is  sufficient  to  calculate  that  one  alone 
and  make  the  others  of  the  same  thickness.  Below  is  given  a 
table  of  liner  thickness  for  various  sized  H.P.  cylinders: 

TABLE   8 


Boiler  pressure                   | 

Boiler  pressure 

Diam- 

Diam- 
eter 

eter 

175 

190 

210 

175 

190 

210 

16 

7 
8 

il 

I 

30 

ItV 

If 

a 

17 

\% 

il 

I 

32 

If 

IT% 

ItV 

18 

T6 

ItV 

34 

ItV 

I^ 

If 

19 

I 

lA 

36 

i^ 

T   5 

J-8 

If 

20 

I 

IT^6 

4 

38 

ItV 

iH 

ill 

21 

ItV 

ItV 

40 

If 

^4 

i| 

22 

lA 

- 1 

^8 

if\ 

42 

iH 

Ijt 

^\i 

23 

li 

■  It? 

li 

44 

if 

^8 

2 

24 

li 

T    3 

Its 

li 

46 

Iff 

iH 

2tV 

25 

lA 

,  1 

irV 

48 

i| 

2 

2\ 

26 

lA 

,  1 
I4 

ItV 

50 

lit 

2rV 

2\ 

28 

li 

T    5 

It^ 

If 

52 

- 

2| 

2f5 

When  a  liner  is  used  the  barrel  can  be  made  \  inch  thinner  than 
the  liner  since  the  liner  must  have  some  extra  thickness  to  allow 
for  reboring.  When  no  liner  is  used  it  is  safer  to  make  the  barrel 
thickness  \  inch  greater  than  the  liner  thickness  given  in  the 
table,  as  a  cracked  cylinder  barrel  is  difficult  to  replace,  while  a 
liner  can  easily  be  renewed. 

The  thickness  of  the  different  walls  are  about  as  follows: 


Thickness  of  metal  in  liner 
Thickness  of  metal  in  barrel 


=  t  (see  table  above). 
=  t  -\"  (with  liner) 
=  ^  +  i"  (without  liner). 


74        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


Thickness  of  metal  in  cylinder  bottom  =  t  (single) 

=  0.9  t  (double). 
Thickness  of  metal  in  cylinder  cover      =  t  (single) 

=  0.85  t  (double). 

=  0.85  /. 

=  t. 


Thickness  of  metal  in  steam  passage 
Thickness  of  metal  in  valve  liners 
Thickness  of  metal  in  cylinder  feet         =  /. 
Thickness  of  metal  in  cylinder-feet  flanges 
Thickness  of  metal  in  cylinder-cover  flange 
Thickness  of  ribs  in  single  cover  or  bottom 
Depth  of  ribs  in  single  cover  or  bottom 


=  1.5  no  1.75/. 
=  1.3  /  to  1.4  /. 

—   ''  16     • 

=  5  /  (at  least). 


Distance  between  double  walls  of  cover  or  bottom  =  5  ^  (at  least). 
Width  of  cylinder  cover  joint 
Diameter  of  bolts  in  cylinder  feet 
Width  of  jacket  space 


Spacing  of  ribs  in  cover  and  bottom 


=  2.75/  to  3.25/. 
=  1.4  /  to  1.6  /. 
=  f  to  I  inch. 
_  100  / 
Vp 


78.   Attachment  of  Liner.  —  The  liner  can  be  held  in  place  in 
several  ways.     One  very  common  method  is  to  have  a  flange 

at  the  lower  end  of  the 
Hner  which  is  bolted  to 
the  cylinder  bottom,  see 
Fig.  39.  This  construc- 
tion makes  the  ports 
longer  than  necessary  and 
can  be  avoided  by  cutting 
off  the  flange  in  the  way 
of  the  port  and  bolting  the 
liner  through  the  barrel. 
Since  this  puts  the  bolts 
in  shear  it  is  not  good 
practice.  The  flange  can 
be  dispensed  with  entirely 
and  the  liner  extended  to  the  cylinder  cover;  thus  the  liner  is 
held  between  the  cover  and  the  bottom  of  the  cylinder  without 
the  use  of  any  bolts.  (See  Plates  2  and  3.)  In  cases  where  the 
liner  does  not  extend  to  the  cyhnder  cover  a  special  packing  is 


Fig.  39. 


DESIGN  OF   ENGINE   PARTS 


75 


provided  to  prevent  leakage  of  steam  at  the  joint  between  the 
barrel  and  the  liner.  The  liner  is  usually  counterbored  at  the 
bottom  and  top  so  that  the  piston  rings  will  over- travel.  The 
amount  of  over-travel  at  the  top  should  be  about  j  inch  and  at 
the  bottom  it  can  be  |  inch. 

79.  Piston  Clearances.  —  The  shape  of  the  cylinder  bottom 
and  the  under  side  of  the  cover  must  conform  to  the  shape  of  the 
piston.  The  length  of  the  cylinder  must  be  such  that  the  linear 
clearances  at  the  top  and  bottom  will  be  about  as  follows: 


Diameter  of  L.P.  cylinder 

Top  clearance 

Bottom  clear- 
ance 

40  inches  and  below 

60  inches 

f  inch 
2  inch 
f  inch 
f  inch 

5  inch 
1  inch 
f  inch 
1  inch 

80  inches 

100  inches  and  above 

80.  Ports  and  Passages. —  The  ports  leading  from  the  cylinder 
to  the  valve  chest  should  be  short  and  direct  in  order  that  the 
clearance  volume  may  be  as  small  as  possible.  In  earlier  designs 
the  ports  were  made  long  and  curved  to  bring  the  valve-chest 
cover  joints  to  the  same  level  as  the  cylinder-cover  joints.  In 
more  recent  design  the  ports  are  made  inclined  or  horizontal  and 
the  valve  chest  extends  above  and  below  the  cylinder.  The  dis- 
tance between  the  end  of  the  piston-valve  liner  and  the  valve- 
chest  cover  must  be  sufficient  to  allow  a  clear  steam  passage  with 
an  area  at  least  equal  to  that  of  the  receiver  pipe  communicating 
with  that  end  of  the  valve. 

The  height  of  the  steam  passage  between  the  cylinder  and  the 
valve  chest  will  depend  upon  the  valve  arrangement  and  the 
steam  speeds  used.  It  is  commonly  made  not  less  than  3  inches 
and  may  vary  from  that  up  to  6  inches.  This  height  is  usually 
increased  about  i  inch  in  the  M.P.  cylinder  and  about  2  inches 
in  the  L.P.  cylinder.  The  cylinder  cover  joint  is  usually  at  the 
same  height  in  all  cylinders  and  is  so  placed  that  in  the  L.P.  cylin- 
der, or  whichever  cylinder  has  the  steam  passage  of  maximum 
height,  there  shall  be  from  3  to  4  inches  of  metal  above  the 
passage  to  allow  the  cylinder  cover  studs  to  be  put  in  without 


76        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

breaking  through  into  the  steam  passage.  The  cross-sectional 
area  of  the  steam  passage  from  the  valve  to  the  cylinder  should 
be  equal  to  the  port  area  through  the  valve  liner.  The  wall  of 
the  passage  around  the  valve  is  generally  circular  in  shape  and 
eccentric  with  the  valve  liner.  The  width  at  the  narrowest  part 
is  made  not  less  than  i|  inches  and  at  other  points  should  be 
sufficient  to  keep  the  steam  speed  constant. 

81.  Cylinder  Openings.  —  Various  openings  into  the  cylinder 
and  valve  chest  must  be  proiided.  In  the  ends  of  each  cylinder 
pro\'ision  must  be  made  for  relief  valves,  and  in  the  lower  end 
there  must  be  an  additional  opening  for  a  cylinder  drain.  This 
drain  should  be  placed  in  the  lowest  part  of  the  steam  passage. 
The  rehef  valve  in  the  lower  end  must  be  so  located  that  it  will 
not  foul  the  connecting  rod  at  the  top  of  its  stroke.  The  indi- 
cator bosses  must  be  so  placed  at  the  top  and  bottom  of  the 
cylinder  that  the  openings  are  not  covered  by  the  piston  at  the 
top  and  bottom  dead  points,  and  they  must  be  far  enough  from 
the  steam  ports  to  prevent  the  pressure  from  being  affected  by 
the  velocity  of  the  steam.  If  jackets  are  used  bosses  must  be 
pro\'ided  for  steam  pipes  leading  to  and  from  them,  and  also  for 
a  drain.  At  some  convenient  point  in  the  steam  passage  "peep 
holes"  must  be  located  to  give  a  view  of  the  openings  in  the  valve 
liner,  by  means  of  which  the  setting  of  the  valve  can  be  deter- 
mined. There  must  be  an  opening  for  a  bottom  drain  in  the 
valve  chest  and  relief  valves  are  placed  either  on  the  chest  or 
on  the  receiver  pipes.  Whenever  the  bosses  are  on  the  barrels 
they  must  be  carried  out  beyond  the  line  of  the  lagging. 

82.  Cylinder  Feet.  —  The  distance  from  the  horizontal 
center  line  of  the  cylinders  to  the  cylinder  feet  is  made  the  same 
in  all  cylinders.  In  the  case  of  the  L.P.  cylinder  the  feet  are 
usually  covered  by  the  cylinder  bottom  and  consequently  must 
be  located  sufficiently  below  the  lower  lagging  flange  to  give 
access  to  the  bolts  and  nuts  making  up  the  joint.  A  distance 
of  8  inches  from  the  lower  lagging  flange  to  the  top  of  the  foot 
flange  will  be  sufficient  for  this  purpose.  The  feet  on  the  other 
cylinders  are  placed  at  the  same  level  as  those  on  the  L.P. 
cylinder. 


DESIGN    OF   ENGINE   PARTS  77 

83.  Boring-bar  Opening.  —  The  opening  in  the  cylinder 
bottom  must  be  large  enough  to  permit  the  use  of  a  good  sized 
boring  bar.  In  the  H.P.  cylinder  the  opening  is  made  as  large 
as  the  construction  will  permit.  The  openings  in  the  M.P.  and 
L.P.  cylinders  are  usually  made  equal  to  about  one-fourth  the 
diameter  of  the  L.P.  cylinder.  The  covers  for  these  holes  carry 
the  piston-rod  packing  and  should  be  made  deep  enough  for  this 
purpose. 

84.  Cylinder-cover  Studs.  —  There  are  two  conditions  which 
determine  the  size  and  number  of  cylinder  cover  studs:  they 
must  have  enough  strength  to  carry  the  load  on  the  cover,  and 
they  must  be  spaced  closely  enough  to  make  the  joint  steam 
tight.  It  is  usual  to  make  the  studs  of  the  same  size  on  all  the 
covers  and  to  determine  the  size  from  the  load  on  the  H.P. 
cylinder;  the  spacing  on  the  other  cylinders  can  be  increased  on 
account  of  the  decreased  steam  pressure.  The  maximum  load 
upon  the  H.P.  cylinder  cover  can  be  found  by  multiplying  the 
boiler  pressure  by  the  maximum  area  of  cover  exposed  to  steam. 
The  bore  of  the  cylinder  at  the  top  will  vary  from  Hd  -f  \  inch 
to  Hd  -{-  ^  inch  according  to  the  size  of  cylinder.  Using  the 
larger  value  the  load  upon  the  cover  will  be 

-(Hd  -f-  -  inch )    X  gage  boiler  pressure. 
4\  2  / 

About  the  smallest  stud  used  in  cylinder  covers  is  i  inch  in  diam- 
eter and  for  any  given  cylinder  the  stud  diameter  will  generally 
be  slightly  greater  than  the  thickness  of  the  liner.  The  diam- 
eter d  can  be  arbitrarily  chosen  and  from  Table  5  the  working 
load  of  that  size  stud  can  be  found.  The  total  load  on  the 
cylinder  cover  di\ided  by  the  working  load  of  one  stud  will  give 
n  the  number  of  studs.  The  pitch  circle  for  the  studs  will  lie  in 
the  middle  of  the  joint  and  if  it  has  a  width  of  3  (/  the  pitch 
circle  will  have  a  diameter 

F  =  Hd-\-h  inch  -f  3  J.  (40) 

Hd  =  diameter  of  H.P.  cylinder. 

The  pitch  of  the  studs  will  be 

n 


78        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

The  pitch  of  studs  on  the  H.P.  cylinder  should  be  from  2.75  </ 
to  3.25  (f.  If  they  are  closer  than  2.75  </  it  will  be  difficult  to 
get  a  spanner  on,  and  if  the  spacing  exceeds  3.25  </  the  joint  is 
apt  to  leak.  If,  with  the  value  of  d  chosen,  the  spacing  is  too 
small  the  value  .of  d  must  be  increased;  if  the  spacing  is  too 
large,  the  value  of  d  must  be  decreased.  On  the  M.P.  and  L.P. 
cylinder  covers  use  the  same  sized  stud,  spaced  4  f/  to  4.5  d  on 
the  M.P.,  and  $d  to  5.5  d  on  the  L.P.  cover.  The  diameter  of 
the  outside  of  the  cylinder  cover  will  be 

G  =  Hd  +  \  inch  +  6  d,  (41) 

if  the  width  of  the  joint  is  taken  as  3  d. 

85.  Valve-chest  Cover  and  Studs.  —  The  valve-chest  covers 
are  usually  held  by  i-inch  studs  spaced  from  4  to  5  inches  apart 
and  the  width  of  the  joint  can  be  made  3  inches.  The  diameter 
of  the  opening  through  the  upper  and  lower  end  of  the  valve 
chest  must  be  large  enough  to  pass  the  valve  liner.  If  the 
diameter  of  the  valve  is  v  and  the  thickness  of  the  liner  is  t  the 
opening  for  the  valve-chest  cover  will  be  about 

V  -\-  2  t  -\-  \  inch, 

and  the  diameter  of  the  valve-chest  covers  will  be 

y  +  2  /  +  6.5  inches. 

When  twin  valves  are  used  the  distance  between  centers  should 
not  be  less  than  1.6  y  -f  i  inch. 

MAIN    BEARINGS 

86.  Character  of  Loads  upon  Bearings.  —  The  diameter  of 
the  crank  shaft  in  the  main  bearings  is  given  by  Formula  (20). 
The  length  of  any  bearing  is  made  such  that  the  bearing  pressure 
shall  not  exceed  that  given  in  Table  6.  The  loads  to  which  the 
main  bearings  are  subjected  increase  as  we  go  towards  the  pro- 
peller, and  differ  in  character.  In  some  cases  the  bearing  pressure 
is  well  distributed  over  the  entire  circumference  of  the  bearing; 
in  other  cases  it  tends  to  act  upon  a  small  portion  only.  Since 
the  important  thing  about  a  bearing  is  that  it  shall  be  sufficiently 
large  to  keep  cool,  it  can  be  seen  that  a  larger  unit  bearing 


DESIGN   OF   ENGINE   PARTS 


79 


pressure  can  be  allowed  where  the  load  is  well  distributed  than 
where  it  is  concentrated  upon  one  part  only. 

When  a  piece  of  shafting,  such  as  a  line  shaft,  for  instance,  is 
transmitting  power  there  is  no  load  upon  the  supports  except 
that  due  to  the  weight  of  the  shafting.  If,  however,  a  crank  is 
introduced  into  the  shaft,  and  a  bearing  is  placed  on  each  side  of 
the  crank,  these  bearings  will  be  subjected  to  loads  in  addition 
to  those  from  weight  alone.  The  force  which  one  web  delivers 
through  the  crank  pin  to  the  other  web  will  be  felt  upon  the 
bearing  adjacent  to  the  latter  web,  while  the  reaction  which  the 
first  web  experiences  will  be  felt  upon  the  bearing  nearest  that 
web.  These  loads  upon  the  bearings  must  be  equal  in  amount 
and  opposite  in  direction,  in  order  that  the  shaft  which  was 
in  equilibrium  before  the 
crank  was  introduced  may 
still  be  in  equilibrium. 

The  turning  force  acting 
at  the  crank  pin  will  in- 
crease as  we  go  towards 
the  propeller,  and,  in  con- 
sequence, this  component 
of  the  bearing  pressure 
will  become  more  pre- 
dominant. The  com- 
ponents of  the  bearing 
pressure  are  shown  in 
Fig.  40.  OA  is  the  posi- 
tion of  the  crank  after  it  has  turned  through  150°.  AB  is  the 
force  acting  through  the  connecting  rod,  and  is  composed 
of  the  weight  and  inertia  of  the  reciprocating  masses  and  the 
unbalanced  steam  pressure  upon  the  piston.  BC  is  the  cross- 
throw  of  the  connecting  rod.  CD  is  the  resultant  of  the  weight 
of  the  shaft  and  the  weight  and  inertia  of  the  connecting  rod. 
DE  is  the  centrifugal  force  arising  from  the  rotation  of  the  un- 
balanced parts  of  the  crank  webs  and  pin.  EF  is  the  force 
acting  upon  the  aft  web,  due  to  the  turning  force  from  the  for- 
ward cylinders.     EG  is  the  reaction  upon  the  forward  web,  due 


Fig.  40. 


8o        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

to  the  above  force.  AF  is  the  resultant  force  acting  upon  the 
aft  bearing,  and  ^G  is  the  resultant  for  the  forward  bearing. 

If  the  turning  force  EF  and  the  reaction  EG  were  left  out,  as 
is  the  case  in  the  bearings  of  the  first  cylinder,  the  two  bearings 
would  be  subjected  to  the  same  load  AE.  The  effect  of  the 
turning  force,  however,  is  to  cause  the  resultant  loads  to  differ 
quite  widely  in  amount  and  in  direction.  Since  the  turning 
force  varies  its  direction  through  360°  during  a  revolution,  its 
effect  upon  the  resultant  as  it  becomes  more  predominant  in  the 
bearings  of  the  crank  shaft  nearer  the  propeller,  is  to  cause  the 
load  to  be  distributed  more  uniformly  around  the  bearing.  In 
the  case  of  the  forward  bearing  of  each  pair  of  bearings,  since  the 
reaction  of  the  turning  force  is,  in  general,  opposed  to  the  direc- 
tion of  the  other  forces,  the  resultant  tends  to  act  upon  the  side 
of  the  bearing.  This  is  shown  very  clearly  in  Fig.  41.  The  full 
lines  give  the  direction  and  intensity  of  the  loads  upon  the  aft 
bearings  and  the  broken  lines  are  for  the  forward  bearings. 

87.  Loads  upon  Main  Bearings.  —  The  mean  load  upon  the 
bearings  can  be  found  approximately  by  means  of  the  formula 

L  =  '^m.V.r-haU.F.c].  (42) 

P.S.  =  piston  speed  in  feet  per  minute. 
H.P.y  =  indicated    horse-power     developed    forward    of 

cylinder  whose  bearings  are  in  question. 
H.P.c  =  indicated  horse-power  developed  in  cyKnder  over 
the  bearings. 
a  =  a.  factor  whose  value   can  be    taken   from   the 
curves  given  in  Fig.  42. 

The  factor  a  allows  for  two  components  of  the  bearing  load, 
one  due  to  the  power  being  developed  in  the  cylinder  over  the 
bearing,  and  the  other  due  to  the  centrifugal  force  of  the  rotating 
parts.  If  we  had  to  deal  with  the  first  component  only,  a  would 
be  constant  for  all  sized  engines,  but  since  the  centrifugal  force 
of  the  rotating  parts  increases  at  a  greater  rate  than  the  horse- 
power of  the  engine,  the  factor  a  will  increase  with  the  size  of  the 
engine. 


Diagrams  Showing  Intensity,  Direction  antl  Distribution  of 
Loatis  ou  the  Main  Bearings  of  the  Engines  of  U.S.S.  Monterey. 
Full  Lines  are  for  Aft  Bearings  of  Cylinder. 
Broken  Lines  are  for  Forward  Bearings  of  Cylimlor. 


1='CYL.   (H.P.) 


2™CYl.   (M.  f.) 


3»°CYL   (UP.) 


FIG.  41 


DESIGN  OF   ENGINE   PARTS 


8l 


Mean   Load  on    BEARiNGS=^p'^g  °  (H.P.^+a  H.P.c) 

H.P.T=-  Horse  Power  Transmitted  from  Forward  Cylinders 
H.P.c=        "  "         Developed  in  Cylinder  over  Bearing 


-10      0        10       20      30      40      50      60       70      80      90      100 
Fig.  42. 


82        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

88.  Centrifugal  Force  of  Crank.  —  The  centrifugal  force 
exerted  by  the  rotating  parts  of  one  crank  will  be  given  approxi- 
mately by  the  following  formula: 

F  =  C(I.H.P.)w25.  (43) 

I.H.P.  =  total  I.H.P.  of  engine. 

n  —  revolutions  per  second. 

5  =  stroke  in  feet. 

C  =  0.5,  solid  forged  shaft 

=  0.83,  built-up  shaft,  Triple  engine 
=  1.1,  built-up  shaft,  Quadruple  engine. 

89.  Combined  Bearings.  —  The  two  bearings  between  ad- 
jacent cylinders  are  sometimes  combined  into  one  bearing.  In 
this  case  the  load  on  the  common  bearing  will  be  a  certain  fraction 
of  the  sum  of  the  loads  which  would  act  upon  the  separate  bear- 
ings. This  fraction  of  the  total  load  is  given  in  the  following 
table : 

TABLE  9 


Bearing  between: 

Type  of  engine 

Angle  between 
cranks 

Factor 

ist  and  2d  cylinders..  < 

2d  and  3d  cylinders.  .  < 
3d  and  4th  cylinders  .  . 

Triple,  high  leading 

Quadruple 

Triple,  low  leading 

Quadruple 

Triple,  high  leading 

Triple,  low  leading 

Quadruple 

120° 
180° 
240° 

9°: 

120° 

240° 

180° 

0.6 

0.4s 

0.85 

0.47 

0.625 

0.9 

0.875 

When  two  cranks  make  an  angle  of  180°  with  one  another, 
with  a  common  bearing  between  them,  the  steam  loads  act  in 
opposite  directions,  and  balance,  if  equal  powers  are  developed 
in  the  two  cylinders.  On  the  other  hand  the  loads  from  the 
turning  forces  transmitted  through  the  crank  pins  are  added  to 
one  another  since  the  common  bearing  serves  as  the  aft  bearing 
of  one  cylinder  and  the  forward  bearing  of  the  other.  Since 
the  cranks  make  an  angle  of  180°,  the  two  forces,  which  in  the 
bearings  of  a  single  crank  are  opposed,  are  in  this  case  added  to 
one  another. 

The  length  of  the  main  bearings  can  be  determined  from  the 


DESIGN  OF  ENGINE   PARTS  83 

load  per  square  inch  that  each  bearing  can  carry,  and  these 
loads  are  given  in  Table  6. 

90.  Crank-pin  Load.  —  The  load  acting  upon  the  crank  pins 
will  be  of  about  the  same  character  as  those  upon  the  bearings 
of  the  first  cylinder.  The  magnitude  of  the  mean  load  will  be 
given  by  the  formula 

i.=  ^i.6Xl.H.P.  (44) 

P.S.  =  piston  speed  in  feet  per  minute. 
I.H.P.  =  indicated  horse-power  developed  in  cylinder  over 
crank  pin. 

The  allowable  pressure  per  square  inch  upon  the  crank  pins 
can  be  from  200  to  250  pounds  in  merchant  engines,  and  from 
300  to  350  pounds  in  naval  engines. 

ENGINE   FRAMING 

91.  Cylinder  Supports.  —  The  cylinder  supports  are  of  four 
kinds:  the  inverted  Y  hollow  casting,  see  Plate  i ;  the  straight  box 
casting,  see  Plate  2;  the  straight  column  of  I-section;  and  the 
steel  column,  sec  Plate  i.  The  supports  for  a  given  engine  may 
be  all  of  one  kind  or  a  combination  of  the  different  types.  The 
framing  as  a  whole  can  be  divided  into  five  classes  depending 
upon  the  combination  of  these  different  types,  (i)  Plate  3 
shows  an  engine  with  the  condenser  forming  a  part  of  the  back 
framing,  the  guides  carried  by  short  box  castings  resting  on  the 
condenser  top,  and  the  front  of  the  engine  supported  by  long 
box  castings.  (2)  Plate  2  shows  an  engine  with  the  cylinders 
supported  by  straight  box  castings  at  front  and  back,  the  back 
supports  carrying  the  guides.  (3)  Plate  i  shows  a  more  open 
type  of  framing  with  inverted  Y  castings  at  the  back  and  steel 
columns  at  the  front.  (4)  Engines  with  large,  heavy  cyhnders 
are  sometimes  supported  by  four  castings,  usually  of  the  open 
I-section.  The  four-slipper  type  of  crosshead  is  used  with  this 
framing.  (5)  This  class  includes  most  naval  and  yacht  engines 
and  the  framing  is  as  shown  by  Plate  4.  These  columns  and 
tie  rods  are  of  wrought  steel  and  give  a  strong,  rigid,  but  expen- 


84        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

sive,  construction.     The  guides  are  carried  by  castings  bolted 

to  the  fore  and  aft  tie  rods,  or  to  the  bottom  of  the  cylinders  and 

to  tie  rods.     The  box  castings  of  the  first  three  classes  are  usually 

made  of  cast  iron,  and  cast  steel  is  used  for  the  fourth  class. 

Where  b'ghtness  is  necessary,  as  in  naval  engines,  the  castings 

of  the  first  three  classes  may  be  of  steel. 

The  thickness  of  metal  for  the  castings  is  not  determined  by 

the  question  of  strength  alone;   castings  must  be  rigid  and  thick 

enough  to  cast  well.     When  made  of  cast  iron  the  thickness  is 

from  I  to  i|  inches;   when  made  of  cast  steel,  from  f  to  i  inch. 

If  the  thickness  is  determined  from  the  load  that  comes  through 

the  connecting  rod  the  working  stress  should  be  about  600  pounds 

for  cast  iron  and  about  1000  for  cast  steel.     The  size  of  the 

wrought-steel   columns  can    be   determined  from    the   Column 

Formula  (12),  or  taken  from  the  curves  of  Fig.  22.     The  length 

of  the  columns  should  be  taken  from  the  assembly  drawing  but 

in  the  case  of  merchant  engines  will  be  from  3  X^*  to  3. 25  X  S. 

The  load  used  in  figuring  them  should  be  the  entire  load  W  not 

W      .  .  .       . 

— ,  since  the  rolling  and  pitchmg  of  the  ship  puts  additional 
2 

stresses  on  the  columns  due  to  the  inertia  of  the  heavy  cylinders. 

92.  Column  Flanges.  —  The  flanges  at  the  foot  of  the  cast 
columns  should  have  a  thickness  of  about  2.25  times  the  thick- 
ness of  metal,  and  the  flanges  at  the  top  should  be  of  the  same 
thickness  as  the  flanges  of  the  cylinder  feet.  The  wrought-steel 
columns  are  attached  to  cylinders  and  bed  either  by  lugs,  as  in 
Plate  I,  or  by  a  circular  flange.  In  the  latter  case  four  bolts  are 
used  and  in  the  former  two.  The  thickness  of  lug  or  flange 
should  be  slightly  greater  than  the  diameter  of  bolt  going  through 
it,  and  the  bolts  should  have  enough  strength  to  carry  the  load 
W.  The  width  of  the  lugs  should  be  sufficient  to  provide  bearing 
surface  for  the  bolt  heads. 

93.  Cylinder-column  Bolts.  —  The  diameter  of  the  bolts  in 
the  cylinder  feet  should  be  from  1.4  to  1.6  the  thickness  of  the 
cylinder  liner  and  there  should  be  enough  bolt  strength  to  carry 
the  load  W.  The  dimensions  of  the  box  casting  at  the  top  should 
be  determined  by  the  breadth  of  the  guide  which  the  column  is 


DESIGN   OF   ENGINE   PARTS 


85 


to  carry  and  there  should  be  enough  flange  space  for  the  bolts 
required.  The  bolts  in  the  top  flange  are  spaced  about  3  diam- 
eters apart  and  the  width  of  the  joint  is  about  3  diameters.  The 
bottom  flange  of  the  cylinder  supports  carries  about  50  per  cent 
more  bolts  than  the  top  flange  and  the  spacing  is  about  4  diam- 
eters. 

94.  Engine  Beds.  —  The  beds  are  made  of  cast  iron  and  cast 
steel  and  have  about  the  same  thickness  as  the  cylinder  supports. 
The  bed  consists  of  two  longitudinal  girders  with  cross  girders 


Fig.  43. 

under  each  main  bearing.  The  shape  of  the  girder  depends  upon 
the  material  used;  if  made  of  cast  iron  they  are  of  the  hollow  box 
form  shown  in  Plates  1,2,  and  3;  if  made  of  cast  steel  the  open 
I-section  is  used,  see  Fig.  43.  The  bed  is  usually  carried  down 
so  that  the  bottom  of  the  holding-down  flange  is  below  the 
lowest  point  in  the  clearance  diagram  of  the  connecting  rod. 
This  will  bring  the  holding-down  flange  about  0.85  stroke  below 
the  center  hne  of  the  crank  shaft.  If  desirable  it  can  be  cut 
away  at  the  sides  as  shown  in  Plate  2.  The  distance  from  the 
top  of  the  side  girders  to  the  lowest  point  of  the  bed  is  about  0.55 


86 


THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


stroke  for  cast-iron  beds,  and  about  0.5  stroke  for  cast-steel  beds. 
The  breadth  of  the  cross  girders  is  always  less  than  the  length  of 
the  bearings  which  they  support.  The  breadth  must  not  be 
made  so  small  that  a  good  casting  cannot  be  obtained,  and  for 
this  reason  it  is  not  always  possible  to  make  the  bearings  for  the 
first  cylinder  as  short  as  the  load  will  permit.  The  breadth  of 
the  cross  girder  should  be  at  least  3  inches  less  than  the  length 
of  the  bearing,  which  it  supports.  The  cross  girders  should  be 
placed  as  close  to  the  crank  webs  as  possible  in  order  that  the 
bending  moment  on  the  shaft  may  be  a  minimum.  In  the 
engine  shown  on  Plate  3  it  will  be  noticed  that  the  valves  have 
been  so  placed  that  the  Marshall  valve  gear  eccentric  has  to 
come  between  the  bearing  and  the  crank  web. 

95.  Main-bearing  Bolts.  —  The  main-bearing  caps  are  held 
by  two  or  more  bolts,  and  the  size  of  these  bolts  should  be  de- 
termined by  the  maximum  load  to  which  the  cap  is  subjected. 
The  mean  loads  were  used  in  obtaining  the  sizes  of  the  main 
bearings,  but  the  maximum  loads  must  be  used  in  finding  the 
thickness  of  the  bearing  caps  and  the  sizes  of  the  bolts.  The 
maximum  load  upon  any  bearing  can  be  found  by  multiplying 
the  mean  load,  as  given  by  Formula  (42),  by  the  following  factors: 


Triple 

Quadruple 

ist  cylinder,  forward  bearing,  factor  = 

2 

2 

aft  bearing,  factor  = 

2 

2 

2d  cylinder,  forward  bearing,  factor  = 

1-75 

1-75 

aft  bearing,  factor  = 

1-75 

1-75 

3rd  cylinder,  forward  bearing,  factor  = 

1.67 

1-75 

aft  bearing,  factor  = 

1-4 

1-75 

4th  cylinder,  forward  bearing,  factor  = 

1.67 

aft  bearing,  factor  = 

1-4 

It  is  best  to  use  one  size  of  bolt  for  all  the  bearings. 

Where  there  is  a  common  bearing  between  two  cranks  the  cap 
is  often  so  broad  that  four  bolts  are  required  to  hold  it  firmly  in 
place.  The  maximum  load  to  which  any  pair  of  bolts  will  be 
subjected  will  be  twice  the  mean  load  when  two  bolts  are  used 
at  the  center  of  the  bearing,  and  1.67  times  the  mean  load  when 
four  bolts  are  used,  one  pair  at  each  end  of  the  bearing. 


DESIGN   OF   ENGINE    PARTS  87 

When  the  main  bearing  is  of  the  t^pe  shown  in  Plates  i  and  3, 
the  bolts  can  be  placed  close  to  the  shaft,  clearing  it  by  f  to  i 
inch.  When  the  t>pe  shown  in  Plate  2  is  used  the  distance 
between  the  bolts  will  be  from  1.5  the  diameter  of  the  shaft  to 
1.75  the  diameter. 

96.  Main -bearing  Caps.  — ■  The  cap  should  be  figured  as  a 

beam  subjected  to  a  bending  moment  of  — ,  where  IV  is  the 

6 

maximum  load  upon  the  bearing  cap  and  /  is  the  distance  be- 
tween the  bolts.  The  breadth  of  the  cap  will  be  2  or  3  inches 
less  than  the  length  of  the  bearing,  or  equal  to  the  breadth  of  the 
cross  girder  supporting  the  bearing.  In  calculating  the  moment 
of  inertia  of  the  section  allowance  should  be  made  for  the  hand- 
hole  which  is  usually  placed  in  the  cap.  The  hand-hole  is  about 
2I  inches  broad  by  5  inches  long.  The  load  upon  the  cap  is 
intermittent  and  a  working  stress  factor  of  about  10  should  be 
used  for  the  sake  of  stiffness. 

The  caps  may  be  made  of  wrought  steel  or  cast  steel.  In  some 
cases  cast  iron  is  also  used.  If  wrought  steel  is  used  the  top 
brass  is  made  separate  and  the  distance  from  the  center  line  of 
the  shaft  to  the  back  of  the  brass  will  be  about  0.67  of  the  diam- 
eter of  the  shaft.  Where  cast  steel  or  cast  iron  is  used  the  thick- 
ness of  the  cap  must  be  increased  by  |  or  i  inch  to  allow  for 
white  metal. 

CYLINDER  ARRANGEMENTS 

97.  Sequence  of  Cylinders.  —  The  arrangement  of  the  cylin- 
ders of  an  engine  having  three  or  more  cranks  will  depend  largely 
upon  the  question  of  balance.  Some  compound  engines  are 
made  with  one  high-pressure  cylinder  and  two  low-pressure 
cylinders,  in  order  that  the  crank  may  be  placed  at  120°  to  give 
a  uniform  turning  moment.  Some  of  the  inchned  engines  used 
upon  paddle  wheel  steamers  have  this  arrangement. 

The  cylinders  and  valves  of  a  three-cylinder  Triple  are  usually 
arranged  as  shown  on  Plate  i.  In  some  cases  the  low-pressure 
cyKnder  is  placed  in  the  center  to  give  a  better  balance.     Plate  2 


88        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

shows  a  compact  design  with  the  valves  placed  at  one  side  of  the 
cylinders  and  run  by  Marshall  valve  gears. 

The  four-cylinder  Triple  is  a  common  type  for  naval  engines. 
The  two  low-pressure  cylinders  usually  develop  less  power  than 
the  others  and  their  reciprocating  parts  are  made  lighter.  These 
lighter  parts  should  be  placed  at  the  ends  of  the  engine,  so  that 
we  have  the  following  arrangement  for  balanced  four-cyUnder 
Triples,  —  forward  L.P.,  H.P.,  M.P.,  and  aft  L.P. 

Quadruple  engines  are  often  arranged  with  the  cylinders  in 
the  sequence  of  their  sizes;  H.P.,  i  M.P.,  2  M.P.,  L.P.  An 
arrangement  which  gives  better  balance  is  to  have  the  H.P. 
cylinder  at  one  end  and  the  i  M.P.  at  the  other  with  the  2  M.P. 
and  L.P.  in  the  middle.  Six-cylinder  Quadruples  are  occasion- 
ally used  on  high-powered  vessels  and  the  usual  practice  is  to 
divide  the  H.P.  cylinder  into  two  cyhnders,  and  the  L.P.  into 
two  cylinders.  These  are  placed  tandem  in  the  middle  of  the 
engine  and  the  i  M.P.  and  2  M.P.  cylinders  are  placed  on  the 
ends. 

98.  Space  Occupied  by  Engines.  —  It  is  often  convenient  to 
know  approximately  how  much  space  an  engine  will  take  up. 
It  will  be  found  that  with  the  usual  arrangement  of  cylinders  and 
valves  on  the  center  line  of  the  engine,  the  length  over  the 
cylinders  will  be  about  i.g'^D  for  merchant  engines  and  about 
i.SHD  for  naval  engines.  Where  the  valves  are  not  on  the 
center  line  the  length  will  be  about  1.65  HZ).  ^D  is  the  sum  of 
the  diameters  of  the  cylinders.  The  length  of  the  engine  bed 
will  be  about  0.85  of  the  length  over  the  cylinders.  The  height 
of  the  engine  from  the  lowest  point  of  the  bed  to  the  top  of  the 
cylinder  covers  will  be  about  5  X  6"  for  naval  engines  where 

-  =  4,  and  from  5.5  X  6"  to  6  X  6"  for  merchant  engines  where 
r 

-  has  a  value  varying  from  4.2  to  4.5.  6*  =  stroke  of  the  engine. 
r 

The  breadth  of  the  engine  bed  will  be  equal  to  about  twice  the 

diameter  of  the  L.P.  cylinder  in  merchant  engines  and  about  1.75 

that  diameter  in  naval  engines. 


DESIGN  OF   ENGINE   PARTS 


89 


VALVE   DIAGRAM 

99.  Eccentricity.  —  The  quantities  usually  known  or  assumed 
before  starting  the  valve  diagram  are  the  mean  cut-off,  ec- 
centricity, leads,  and  steam  speeds.  The  mean  cut-off  is  de- 
termined by  the  desired  distribution  of  power  and  the  other 
quantities  are  assumed.  The  eccentricities  used  upon  marine 
engines  vary  from  3  to  5I  inches,  depending  upon  the  size  of 
engine  and  the  steam  speeds  employed,  and  will  have  about  the 
following  values  for  different  sized  engines: 


I.H.P.  of  engine 

500 

to 
1000 

1000 
to 
2000 

2000 
to 
Sooo 

5000 

to 

10,000 

Eccent.  of  H.P.  and  M.P.  cylinders 
Eccent.  of  L.P.  cylinder 

3  t0  3i 
3  t0  3f 

3?  t0  4 
3i  to  4i 

4  to  4I 
4  to  5 

4^  to  5 
42  to  sh 

100.  Steam  Speeds.  —  The  steam  speeds  in  feet  per  minute 
should  be  about  as  follows: 

Merchant  Naval 

Main  steam  pipe 6500        7000 

Throttle  valve 6000        6500 

H.P.  M.P.  L.P. 

Entering  steam 6000         7500         10500 

Exhaust  steam 5000         6500  7500 

Exhaust  to  condenser 6500         ....  .... 

In  some  naval  engines  the  steam  speeds  at  maximum  power 
will  be  slightly  higher  than  these. 

101.  Width  of  Ports.  —  The  maximum  port  opening  will  be 
determined  from  the  valve  diagram,  and  the  width  of  port  will 
be  determined  by  the  ratio  of  the  speed  of  the  entering  steam  to 
the  speed  of  the  exhaust  steam. 

Width  of  port  — 

r         .  ^  .        _  speed  of  entering  steam 

mean  01  maximum  port  opemngs  X  -^ — : — - — , 

speed  of  exhaust  steam 

The  width  of  port  should  be  from  0.6  of  the  eccentricity  to 
0.75  of  the  same,  although  if  the  cut-off  is  quite  long  the  ratio 


90       THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

may  run  as  high  as  0.85.  If  the  width  does  not  come  within 
these  Umits  the  assumed  values  of  the  steam  leads  should  be 
changed. 

102.  Steam  Lead.  —  The  valves  of  marine  engines  are  de- 
signed with  greater  steam  leads  than  those  of  land  engines.  The 
ratio  of  steam  lead  to  eccentricity  is  ordinarily  0.13  for  the  top 
end  of  the  H.P.  cylinder  valve,  and  about  0.16  for  the  top  end  of 
the  L.P.  cylinder  valve.  The  ratio  may  be  greater  than  these 
if  the  cut-off  is  short.  The  steam  lead  on  the  bottom  end  of  the 
valve  is  usually  greater  than  that  on  the  top  by  an  amount  vary- 
ing from  jQ  to  Ye  inch,  for  valves  taking  steam  on  the  ends, 
and  greater  by  an  amount  varying  from  jq  to  |  inch  for  valves 
taking  steam  in  the  middle.  The  difference  is  made  less  in  the 
latter  case  because  the  wear  of  the  joints  in  the  valve  gear  in- 
creases this  difference,  while  in  valves  taking  steam  on  the  ends 
the  effect  of  wear  is  to  decrease  the  original  difference.  The 
valve  of  the  H.P.  cylinder  should  always  take  steam  in  the 
middle,  while  in  the  L.P.  cylinder  the  valves  should  take  steam 
on  the  ends.  The  intermediate  valves  may  be  made  either 
way. 

103.  Size  of  Piston  Slide  Valve.  —  The  diameter  of  the  piston 
slide  valves  can  be  found  by  the  following  formula: 

'^-^^x^'  (45) 

d  should  not  be  less  than  4  c  w. 
d  =  diameter  of  valve  in  inches. 
D  =  diameter  of  cylinder  in  inches. 
P.S.  =  piston  speed  in  feet  per  minute. 

c  =  portion  of  entire  circumference  of  liner  available  for 
clear  port  opening,  and  is  about  0.75  in  merchant 
engines  and  about  0.85  in  naval  engines. 
X  =  speed  of  exhaust  steam  in  feet  per  minute. 
w  =  width  of  port  in  inches. 

If  d  is  less  than  4  c  w  the  area  bounded  by  the  inner  circum- 
ference of  the  hner  will  be  less  than  the  area  through  the  ports. 


DESIGN   OF   ENGINE   PARTS 


91 


104.    Size  of  Flat  Slide  Valve.  —  The  breadth  of  the  flat  slide 
valve  can  be  found  by  means  of  formula  (45)  if  we  multiply  both 
sides  by  tt  and  let  c  =  i. 
7rZ)2  X  P.S. 


b  = 


^Xw 


(46) 


b  =  clear  breadth  of  port  of  flat  slide  valve. 

It  will  be  necessary  to  put  in  i-inch  ribs  about  every  16  inches, 
so  the  total  breadth  will  have  to  be  increased  to  allow  for  these 


Bot.  Cut-off/' 


Top  Cut-off 


Bottorrt 
Fig.  44. 

ribs.  If  the  breadth  is  more  than  0.95  D  it  will  be  necessary  to 
use  a  double-ported  valve,  and  if  this  makes  the  valve  long  and 
narrow  the  eccentricity,  and  consequently  w,  can  be  decreased. 
105.  Valve  Diagram.  —  The  valve  diagram  from  which  the 
maximum  port  opening,  angle  of  advance,  steam  laps,  and  ex- 
haust laps  are  determined  can  be  drawn  as  shown  in  Fig.  44. 
The  circle  A  BCD  has  a  radius  equal  to  the  eccentricity.     Place 

AF 
the  pomt  F  so  that  -— ;:;  =  mean  cut-ofT.     Erect  the  perpendic- 

ular  FG.     At  A  describe  an  arc  whose  radius  is  equal  to  the 


92        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

mean  of  the  steam  leads  of  the  two  ends.  Draw  GH  tangent  to 
this  arc  and  draw  a  line  JK  through  O  perpendicular  to  GH. 
The  angle  BOJ  will  be  the  angle  of  advance.  At  A  and  C  draw 
the  lead  circles  as  shown  in  full  lines,  the  radius  of  each  being 
equal  to  the  steam  lead  at  that  end.  Draw  the  lines  LM  and 
NP  tangent  to  the  lead  circles  and  perpendicular  to  JK.  Draw 
lines  OL,  OM,  ON,  and  OP.  These  Unes  represent  the  crank 
position  for  admission  and  cut-off  at  top  and  bottom.  OQ  and 
OR  will  be  the  steam  laps  and  QJ  and  RK  the  maximum  port 
openings.  The  percentage  of  the  stroke  traversed  by  the  piston 
at  the  time  of  cut-off  can  be  determined  by  swinging  from  L 

and  P  with  a  radius  equal  to  OA  X  -  • 

r 

The  release  and  compression  of  the  steam  on  the  top  side  of 
the  piston  will  occur  at  about  the  right  time  relative  to  the  other 
events  if  the  exhaust  lap  is  made  zero,  thus  causing  the 
events  to  occur  at  mid-position  of  the  valve,  OS  and  OT.  The 
release  of  the  steam  on  the  under  side  of  the  piston  should  occur 
2  or  3  per  cent  of  the  stroke  earlier  than  the  release  on  the  top 
side;  i.e., 

Au'    cy 


AC       AC 


+  0.02. 


UV  ia  perpendicular  to  JK  and  the  distance  OW  is  the  exhaust 
lap  for  the  bottom  of  the  valve. 

The  relation  between  the  angle  of  advance,  eccentricity,  mean 
cut-off,  and  mean  lead  is  given  by  the  following  equation: 


J        I 

cos  8  =  — 


V4e'B-a'--a\/^-^'^'  (47) 


2  e 

e  =  eccentricity. 
B  =  mean  cut-off  (decimal). 
a  =  mean  lead. 

The  results  obtained  graphically  should  be  checked  by  the  above 
formula.  It  should  also  be  true  that  steam  lap  -f  lead  = 
e  sin  5. 

The  results  should  be  collected  into  a  table  of  the  following 
form: 


DESIGN  OF   ENGINE   PARTS 


93 


TABLE   10 
Diameter  of  Cylinders  and  Stroke 

Scale  of  valve  circle. 

Ratio  of  connecting  rod  to  crank   (  -  J- 


H.P. 

M.P. 

L.P. 

Eccentricity 

Top 

Bottom 

Top 

Bottom 

Top 

Bottom 

Width  and  length  of  port 

Steam  lap     

Exhaust  lap 

Angular  advance 

Steam  lead,  linear 

Cut-off,  in  decimal  of  stroke 

Exhaust  lead,  in  decimal  of  stroke. 
Compression,  in  decimal  of  stroke.. 
Maximum  port  opening 

Velocity  of  steam,  feet  per  min.  .  .  . 
Velocity  of  exhaust,  feet  per  min. .  . 

When  the  valves  take  steam  at  the  middle  the  valve  diagram 
is  drawn  the  same  as  for  valves  taking  steam  at  the  ends,  but  the 
eccentrics  are  set  270°  +  angle  of  advance  ahead  and  back  of 
the  crank  instead  of  90°  +  angle  of  advance. 


VALVES   AND   VALVE   GEAR 

106.  Piston  Valves.  —  Piston  valves  are  made  solid,  as  shown 
in  Plate  2,  or  hollow,  as  shown  in  Plate  3.  They  are  made  hollow 
when  it  is  desired  to  have  one  pipe  supply  steam  to  both  ends  of 
the  valve,  and  the  area  through  the  middle  of  the  valve  should 
equal  the  area  through  the  pipe.  The  length  of  the  valve 
depends  upon  the  location  of  the  valve  liners,  which  are  placed 
a  sufficient  distance  from  the  top  and  bottom  of  the  valve  chest 
to  allow  the  steam  to  enter  and  get  away  from  the  ends  wathout 
the  area  for  steam  passage  being  restricted.  The  liners  should 
be  placed  as  near  the  ends  as  possible,  and  the  passage-ways  to 
the  cylinder  made  as  direct  as  possible,  in  order  to  reduce  the 


94        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

clearance  space.  The  length  of  the  liners  should  be  such  that 
the  piston-valve  rings  will  not  spring  out  at  the  extremities  of 
the  stroke.  The  Hners  should  be  counterbored  at  the  ends 
sufficiently  to  allow  the  rings  to  over-travel  |  inch  or  more. 
The  length  of  the  piston- valve  Hner  =  width  of  port  +  steam 
lap  +  exhaust  lap  +  the  travel  of  the  valve. 

107.  Load  upon  Valve  Stems.  —  The  valve  stems,  eccentric 
rods,  and  links  must  be  designed  to  take  care  of  the  frictional 
load,  the  inertia,  and  the  weight  of  the  valves.  In  addition,  if 
a  single  valve  is  used  with  a  guide,  such  as  shown  in  Plate  2, 
the  stem  below  the  valve  must  be  designed  for  the  bending  that 
may  come  upon  it  from  the  pull  of  the  drag  rods  in  reversing 
when  the  valve  is  at  its  lowest  point  in  the  stroke. 

In  the  case  of  the  flat  valve,  the  frictional  load  can  be  calcu- 
lated from  the  area  of  the  surfaces  in  contact  and  the  unbalanced 
pressure  upon  the  back  of  the  valve,  no  allowance  being  made 
for  any  balancing  device.  The  piston  valve  is  not  subjected 
to  any  load  due  to  unbalanced  pressure,  but  the  friction  of  the 
rings  and  the  stuffing-box  must  be  allowed  for.  It  is  usual  to 
assume  that  this  load  is  some  multiple  of  the  weight  of  the  valve, 
valve  stem,  crosshead,  and  block.  If  this  load  is  taken  as  three 
times  the  weight  of  the  above  parts,  a  reasonable  allowance  will 
be  made. 

The  inertia  of  the  valves  is  calculated  upon  the  assumption 
of  harmonic  motion,  and  the  maximum  inertia,  at  the  beginning 
and  end  of  the  stroke,  is  used.  The  formula  which  gives  this 
inertia  is 

F  =  0.000,028,37  WRm,  (48) 

where     W  =  weight  of  valve  or  valves,  valve  stem,  crosshead, 
and  block,  usually  for  the  low-pressure  gear; 

R  =  eccentricity  in  inches; 
and  N  =  revolutions  per  minute. 

In  the  case  of  piston  valves,  the  load  for  which  the  valve  stem 
should  be  figured  will  be 

L  =  W  {a  +  0.000,028,37  ^^^),  (49) 


DESIGN   OF   ENGINE   PARTS  95 

if  no  balance  piston  is  used;  and 

L  =  PF  (3  +  0.000,028,37  RN'),  (50) 

if  a  balance  piston  is  used. 

If  balance  pistons  are  used  which  balance  more  than  the 
weight  the  load  can  be  still  further  decreased. 

In  the  case  of  flat  valves  the  load  upon  the  valve  stems  will  be: 

L  =  pAf+W(i+  0.000,028,37  RN'),  (51) 

if  no  balance  piston  is  used;  and 

L  =  pAf  +  0.000,028,37  WRN^,  (52) 

if  a  balance  piston  is  used. 

p  =  the  unbalanced  unit  pressure  upon  valve; 
A  =  area  exposed  to  unbalanced  pressure; 
/  =  coefficient  of  friction,  usually  taken  as  0.2; 
W,  R,  and  A^  are  as  above. 

The  portion  of  the  valve  stem  between  the  valve  and  the  link 
block  in  the  case  of  single  valves,  and  between  the  piston  valve 
and  the  yoke  in  the  case  of  twin  valves,  should  be  figured  by 
means  of  the  piston-rod  formula;  the  portion  of  the  stem  within 
the  valve  should  be  figured  for  tension  only,  as  the  stem  is 
shouldered  down  where  it  enters  the  valve,  and  the  thrust  is 
carried  by  this  shoulder. 

108.  Valve-stem  Bending.  —  The  load  L  is  carried  by  the 
links,  and  when  the  latter  are  at  an  angle  with  the  horizontal  (see 
Fig.  45)  there  will  be  a  tendency  for  the  block  to  slide  along  the 
links.  As  the  valve  stem  is  kept  from  mo\ang  by  the  valve  stem 
guide,  this  tendency  results  in  a  bending  moment  upon  the  valve 
stem,  and  a  reaction  in  the  drag  rods.  The  maximum  angle 
that  the  links  make  with  the  horizontal  is  assumed  to  be 

.  _,      2  E  sin  (go  —  d)  ^     . 

sin  ^=  b ^^^^ 

E  =  eccentricity  of  valve. 

d  =  angle  of  advance. 

b  =  distance  between  eccentric  rod  pins,  usually  =  6  E. 


96        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 
The  component  which  bends  the  valve  stem  will  be 


P  = 


L  2  E  sin  (90°  —  d) 


(54) 


The  bending  moment  upon  the  valve  stem  will  be  if  =  PI,  and 
/  is  the  distance  from  the  bottom  of  the  valve  stem  guide  to  the 


Fig.  45. 

lowest  point  in  the  travel  of  the  link  block.  For  twin  valves, 
with  the  stems  yoked  together,  the  bending  moment  would  act 
upon  the  yoke,  which  always  has  plenty  of  strength. 


DESIGN   OF   ENGINE   PARTS  97 

109.  Drag  Rods.  —  If  the  eccentric  rod  were  normal  to  the 
link  at  the  time  when  the  latter  makes  its  maximum  angle  with 
the  horizontal  (see  Fig.  45)  the  load  P  would  be  all  that  the  drag 
rods  would  have  to  carry;  but  since  the  eccentric  rod  is  in  line 
with  the  valve  stem  at  that  time,  a  portion  of  the  load  normal 
to  the  links  will  come  upon  the  drag  rods  in  addition  to  the  com- 
ponent along  the  links.  In  the  diagram  accompanying  Fig.  45, 
^0  is  the  load  L  acting  through  the  valve  stem.  This  load  is 
resolved  into  BO  along  the  links  and  AB  normal  to  the  links. 
Since  the  eccentric  rod  is  in  the  position  OD,  the  load  OC  =  AB, 
normal  to  the  links,  is  resolved  into  CD  and  OD.  The  drag  rods 
have  to  take  care  of  BO  +  CD  =  2  P,  and  the  eccentric  rod  is 
subjected  to  the  load  L.  Although  the  drag  rods  are  not  exactly 
parallel  to  the  links  in  the  position  shown,  the  load  upon  the  rods 
will  be  practically  2  P,  so  that  each  rod  should  be  designed  for 
the  load  P. 

110.  Yokes.  —  The  yokes  should  be  figured  as  beams  sup- 
ported at  the  ends  and  loaded  at  the  middle  with  the  load  L. 
The  surface  of  the  valve-stem  guide  in  the  case  of  single  valves, 
and  of  the  valve-yoke  guide  in  the  case  of  twin  valves,  should  be 
such  as  to  keep  the  unit  bearing  pressure,  due  to  the  load  P, 
between  70  and  100  pounds. 

111.  Eccentric  Rods.  —  The  diameter  of  the  eccentric  rods 
and  drag  rods  at  the  middle  should  be  figured  by  the  connecting- 
rod  formula,  as  they  are  columns  hinged  at  the  ends.  The 
diameter  of  the  drag  rods  at  the  ends  can  be  made  three-fourths 
of  their  diameter  at  the  middle.  The  diameter  of  the  eccentric 
rods  at  the  top  should  be  0.9,  and  at  the  bottom  i.i  of  the  diam- 
eter at  the  middle.  The  length  of  the  drag  rods  is  usually  from 
15  £  to  18  £,  and  of  the  eccentric  rods  20  £  to  30  £  for  merchant 
engines  and  155  to  20  E  for  naval  engines.  The  diameter  of 
the  bolts  in  the  caps,  etc.,  should  be  such  as  to  carry  the  loads 
with  the  working  stresses  given  in  Table  5. 

112.  Link  Bars.  —  The  link  is  usually  of  the  double-bar  type, 
Fig.  46,  and  is  figured  as  a  beam  supported  at  the  ends  and 
loaded  at  the  middle  with  the  load  L\  as  mentioned  before,  the 
length  of  the  beam,  or  distance  between  eccentric  rod  pins,  a,  is 


98        THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


usually  6  E.  The  breadth  of  the  bars,  h,  is  usually  about  one- 
third  of  the  depth,  c,  and  the  depth  is  so  chosen  that  the  working 
stress  factor  will  be  12,  as  the  load  is  alternating.  Making  this 
assumption  in  regard  to  the  relation  of  breadth  and  depth,  the 
formula  for  the  depth  of  each  link  bar  becomes 


h 


'gLa 

4/' 

L  =  load  upon  valve  gear. 
a  =  distance  between  eccentric  rod  pins. 
/  =  allowable  stress  with  factor  of  12. 


(55) 


T 


^-il^ 


Tmj 


m 


Fig.  46. 


113.  Link-block  Pin.  —  The  diameter  d  of  the  link-block  pin, 
Fig.  47,  is  from  0.9  to  i.o  of  the  depth  of  the  bar,  c;  the  diameter 
of  the  eccentric-rod  pins,  e,  Fig.  46,  is  about  three-fourths  the 
depth  of  the  link  bar,  and  the  diameter  of  the  drag-link  pin,/,  is 
about  three-fourths  the  diameter  of  the  eccentric-rod  pin.  The 
lengths  of  all  these  pins,  as  well  as  that  of  the  block  gibs,  g,  must 
be  such  as  to  keep  the  bearing  pressures  uithin  the  limits  given 
in  Table  6.  The  thickness  of  the  metal,  h,  joining  the  link- 
block  pin  at  the  sides  to  the  sliding  gibs  should  be  from  0.25  to 
0.3  of  the  diameter  of  the  link-block  pin,  d. 


DESIGN  OF  ENGINE   PARTS 


99 


114.   Eccentrics.  —  The  diameter  of  the  eccentric  will  be 

D  =  2{r  +  E-\-c).  (56) 

E  =  the  eccentricity. 
r  =  radius  of  eccentric  pad  on  crank  shaft. 

c  =  - ,  if  the  lower  part  of  the  eccentric  is  made  of  cast  iron 
3 

T     .     .     . 

=  - ,  if  it  is  made  of  cast  steel. 
4 

The  upper  part  of  the  eccentric.  Fig.  48,  is  always  made  of  cast 
iron,  and  is  joined  to  the  lower  part  by  bolts  or  collar  studs.     The 
keyway  should  be  cut  on  a 
hne  at  right  angles  to  the  'n"-~^~n' 

joint  of  the  two  parts,  so 
that  the  eccentric  can  be 
readily  taken  off.  If  the 
eccentric  is  so  situated  that 
it  can  be  moved  along  the 
shaft  clear  of  the  key,  then 
the  keyway  can  be  on  the  side,  as  shown  dotted  in  Fig.  48,  and 
the  set  screw  w^ll  be  more  conveniently  located. 

It  is  well  to  make  the  keyway  considerably  broader  than  the 
key  in  the  shaft,  and  to  lit  liners  on  either  side,  so  that  slight 


S^ 


1- 


"W 


^ 


Fig.  47. 


b 


Fig.  48. 


Fig.  49. 


changes  can  be  made  in  the  angular  advance,  if  it  is  thought  best. 
The  breadth  of  the  eccentric  should  be  sufficient  to  keep  the 
bearing  pressure  within  the  Hmits  given  in  Table  6. 


TOO     THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

115.  Eccentric  Strap.  —  The  eccentric  strap,  Fig.  49,  should 
have  lips  fitting  on  each  side  of  the  bearing  surface  of  the  eccentric 
sheaves,  to  keep  the  strap  in  place.  The  strap  bolts  should  be 
designed  to  carry  the  load  L  coming  upon  the  valve  gear,  as 
should  also  the  bolts  uniting  the  eccentric  rod  to  the  strap.  The 
straps  are  usually  made  of  cast  steel  lined  mth  white  metal,  and 
the  section  of  the  lower  half,  exclusive  of  the  white  metal,  should 
be  sufficient  to  carry  the  load  L  with  a  working  stress  factor  of  8. 

116.  Reverse-shaft  Levers.  —  The  reverse-shaft  levers,  Fig. 
45,  should  be  figured  for  the  load  2  P  upon  the  drag  rods,  and 
should  be  of  such  a  length  that  the  angle  moved  through  is 
not  more  than  80°.  The  "gag"  upon  the  lever  should  be  so 
arranged  that  in  the  backing  position  the  center  fine  of  the  screw 
is  vertical.  Tliis  will  cause  the  position  of  the  Hnk  when  back- 
ing to  be  practically  the  same,  irrespective  of  the  position  of  the 
end  of  the  drag  rod  in  the  slot.  In  the  ahead  position  of  the 
lever  the  gag  screw  will  be  nearly  horizontal,  and  the  link  can  be 
pulled  in  an  amount  about  equal  to  the  travel  of  the  nut  on  the 
thread. 

117.  Reverse  Shaft.  —  The  reverse  shaft  should  be  figured 
for  torsion  and  bending,  due  to  the  thrust  of  the  drag  rods.  As 
it  is  not  always  possible  to  get  the  bearings  close  to  the  various 
reverse  shaft  levers,  the  bending  moment  may  be  large  in  these 
shafts.  The  equivalent  twisting  moment  should  be  found  by 
Formula  (15).  The  twisting  moment  T  used  in  this  formula 
should  be  that  coming  upon  the  portion  of  the  reverse  shaft 
nearest  the  reversing  engine.  The  reversing  engine  is  usually 
placed  near  the  middle  of  the  length  of  the  main  engine,  and  it  is 
generally  safe  to  figure  the  shaft  for  the  twisting  moment  neces- 
sary to  move  the  low-pressure  gear;  for  when  these  links  make 
the  greatest  angle  \\ath  the  horizontal  plane  the  other  Hnks  are 
in  a  more  advantageous  position.  In  the  prelimmary  design 
the  bending  moment  can  be  neglected,  and  the  working  stress 
factor  increased  from  12  to  15  to  allow  for  this  neglect.  After 
taking  off  the  medium-pressure  reverse-shaft  levers,  the  size  of 
the  shaft  running  to  the  high-pressure  levers  can  usually  be 
decreased. 


DESIGN  OF  ENGINE  PARTS  lOl 

118.  Valve  Stem  Load.  —  In  using  Formula  (48),  the  weight 
of  the  valves,  valve  stems,  crossheads,  and  blocks  is  usually 
obtained  from  data  for  similar  engines.  If  no  such  data  are 
available  the  loads  coming  upon  the  valve  stems  can  be  taken  as 
15  DE.  D  is  the  diameter  of  the  valve  in  inches  and  E  is  the 
eccentricity  in  inches.  In  the  case  of  twin  valves  the  sum  of 
the  diameters  should  be  used. 


SECTION  III 
ENGINE  BALANCING 

119.  Vertical  Forces  Balanced.  —  The  unbalanced  forces 
which  are  most  objectionable  in  a  marine  engine  are  those  which 
act  in  a  vertical  direction.  The  ship  is  usually  much  stififer  in -a 
horizontal  plane  than  it  is  in  a  vertical  plane  and  as  the  horizontal 
disturbing  forces  with  an  upright  engine  are  a  good  deal  smaller 
than  the  vertical  forces,  attention  is  confined  almost  entirely  to 
the  vertical  disturbing  forces. 

120.  Motion  of  Parts.  —  The  moving  parts  of  an  engine  may 
be  divided  into  four  classes  depending  upon  the  character  of  the 
motion  of  the  part.  Some  parts  reciprocate,  some  rotate,  some 
vibrate,  and  some  both  reciprocate  and  vibrate.  The  piston, 
piston  rod,  crosshead,  slipper,  valves,  and  valve  stems  have  a 
reciprocating  motion;  the  crank  shaft,  crank  webs,  crank  pins, 
and  eccentrics  have  a  rotating  motion;  the  drag  rods  and  pump 
levers  vibrate;  the  connecting  rods  and  links  both  vibrate  and 
reciprocate.  The  calculations  for  balancing  the  vertical  forces 
would  become  too  compHcated  if  we  attempted  to  treat  the 
motion  of  each  part  with  absolute  correctness;  so  it  is  usual  to 
group  all  parts  into  two  classes,  one  rotating  and  the  other 
reciprocating- 

121.  Division  of  Connecting  Rod.  —  In  order  that  this  classi- 
fication may  be  made  it  is  necessary  to  assume  that  the  con- 
necting rod  can  be  divided  into  two  parts,  one  a  reciprocating 
part  acting  at  the  crosshead  and  the  other  a  rotating  part  acting 
at  the  crank  pin. 

Let      M  =  mass  of  the  rod. 

/  =  distance  between  centers. 

X  =  distance  from  crosshead  to  center  of  gravity  of 
rod. 


ENGINE   BALANCING  103 

I  —  X 


Then  the  mass  acting  at  the  crosshead  is  taken  as  M 


I 


X 

and  the  mass  acting  at  the  crank  pin  is  M  - .     This  is  equivalent 

to  assuming  that  the  resultant  of  the  vertical  accelerating  forces 
acts  at  the  center  of  gravity  of  the  rod  throughout  the  revolution, 
or  that  the  connecting  rod  is  of  infinite  length.  As  a  matter  of 
fact  the  resultant  of  the  vertical  accelerating  forces  does  not  act 
at  the  center  of  gravity  of  the  rod  but  is  acting  sometimes  above 
and  sometimes  below  that  point  at  various  parts  of  the  stroke 
(see  Fig.  50).  A  consideration  of  the  velocities  of  the  different 
parts  of  the  rod  in  a  vertical  direction  will  show  this  to  be  true. 
Professor  Lanza  gives  the  following  formula  for  the  distance 
from  the  crosshead  to  the  point  of  appUcation  of  the  resultant  of 
the  vertical  accelerating  forces: 

/i  =  acceleration  of  crosshead. 

/2  =  acceleration  of  crank  pin  in  a  vertical  direction. 

/  =  length  of  rod  between  centers. 

p  =  distance  from  crosshead  to  center  of  percussion. 

X  =  distance  from  crosshead  to  center  of  gravity. 

122.  Error  in  Division  of  Connecting  Rod.  —  Fig.  50  is 
plotted  by  means  of  this  formula  on  the  supposition  that  the 
ratio  of  connecting  rod  to  crank  is  4,  that  x  =  0.62  /,  and  that 
p  =  0.96  /.  The  horizontal  line  BB  shows  the  assumption  made 
in  regard  to  the  point  of  application  of  the  resultant  of  the  ac- 
celerating forces  and  the  curves  D  show  the  actual  location  of  that 
point.  In  Fig.  51  curves  are  given  which  show  the  acceleration 
of  the  ends  of  the  connecting  rod  and  also  the  acceleration  of  its 
center  of  gravity.  Where  the  acceleration  of  all  three  points  is 
the  same  the  rod  has  a  motion  of  translation  and  the  accelerating 
force  is  applied  at  the  center  of  gravity  of  the  rod.  This  occurs 
at  crank  angles  of  45°  and  135°.  When  the  acceleration  of  the 
crosshead  end  of  the  rod  is  zero  the  accelerating  force  is  applied 
at  the  center  of  percussion.     When  the  acceleration  of  the  center 


I04     THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


Figs,  so,  51. 


ENGINE   BALANCING 


105 


of  gravity  of  the  rod  is  zero  and  when,  consequently,  the  acceler- 
ating force  is  zero,  the  point  of  application  is  at  infinity.  Thus 
the  maximum  deviation  from  the  assumed  condition  occurs  at  a 
time  when  the  force  itself  is  a  minimum.  The  deviation  of  the 
assumed  condition  from  the  truth  is  shown  by  curve  E  plotted 
upon  AA  as  a  base.  From  0°  to  45°  we  have  assumed  more 
weight  acting  at  the  crank  pin  than  we  should,  while  from  45° 
to  about  85°  we  have  assumed  less. 

This  assumption  in  regard  to  the  portions  of  the  connecting 
rod  that  shall  be  considered  as  acting  at  the  crosshead  and  crank 
pin  gives  us  the  following  rotating  masses :  —  crank  pin,  crank 


webs,   and  a  portion  of  the  connecting  rod,  M-. 

V 


The  valve 


gears  are  also  treated  as  rotating  masses  for  reasons  that  will 
appear  later.  The  reciprocating  masses  will  be,  —  the  piston, 
piston  rod,  crosshead,  slipper,  and  the  remainder  of  the  con- 
necting rod,  M — - — 

123.   Balance  of  Rotating  Masses.  —  It  is  not  at  all  difficult 
to  balance  the  rotating  masses,  as  it  is  only  necessary  to  find  the 


Ai 


1.— -    " 

--"-"" 

Fig.  52. 


resultant  of  these  masses  and  then  to  so  place  other  rotating 
masses  that  this  resultant  shall  be  reduced  to  zero.  It  is  usual 
to  do  this  by  placing  one  or  more  weights  on  the  crank  webs  at 
either  end  of  the  engine.  The  resultant  can  be  found  by  graphi- 
cal means,  as  shown  in  Fig.  52.  Let  the  unbalanced  mass  be 
represented  in  magnitude  by  OR  and  let  the  balance  weights  be 
placed  in  the  planes  A  A  and  BB.  Project  the  length  OR  upon 
the  plane  BB  and  draw  AB.  This  diagonal  hne  will  divide  OR 
into  two  parts,  such  that,  if  OC  is  placed  in  the  plane  BB,  and  CR 


Io6     THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

in  the  plane  AA,  acting  in  a  direction  opposite  to  OR,  the  moment 
of  OC  about  O  will  be  equal  to  the  moment  of  CR  about  O,  and 
we  shall  have  OR  balanced  for  hammering  and  tilting.  If  the 
mass  to  be  balanced  is  not  between  the  two  balance  planes 
the  construction  shown  in  Fig.  53  can  be  used.     In  this  case  the 


B 


Fig.  53. 

mass  acting  at  ^^  is  greater  than  the  mass  at  O  and  acts  in  the 
opposite  direction,  while  the  mass  at  BB  is  equal  to  the  difference 
of  these  two  and  acts  in  the  same  direction  as  OR. 

This  method  can  be  applied  to  an  engine  with  any  number  of 
cylinders.     In  Fig.  54  it  is  applied  to  a  three-crank  engine  with 


Fig.  54. 

cranks  at  120°.  In  each  balance  plane  there  will  be  three  com- 
ponents to  be  combined  at  the  proper  angles,  and  the  balance 
mass  must  be  equal  to  the  resultant  and  act  in  an  opposite 
direction.     See  Figs.  55  and  56. 

When  the  unbalanced  masses  are  not  rotating  on  a  radius 


ENGINE   BALANCING 


107 


equal  to  the  length  of  the  crank  arm  it  is  usual  to  reduce  them  to 
equivalent  masses  acting  at  tliis  radius  by  means  of  the  following : 


AA 
Fig.  55. 

equivalent  mass  X  crank  arm  length  = 
actual  mass  X  arm  of  center  of  gravity. 
In  the  case  of  the  crank  webs  a  certain 
portion  is  balanced  because  of  its  con- 
struction and  only  the  unbalanced  portion 
need  be  considered. 

124.  Aeceleration  of  Crosshead.  —  The 
rotating  masses  will  be  balanced  not  only 
for  forces  acting  in  a  vertical  plane  but 
also  for  forces  in  a  horizontal  plane. 
When  we  come  to  the  reciprocating 
masses,  however,  we  have  to  deal  with 
forces  which  act  in  a  vertical  plane  only. 
It  is  usual  to  consider  that  the  speed  of 
rotation  of  the  crank  shaft  is  uniform. 
The  end  of  the  connecting  rod  which  is 
attached  to  the  crank  pin  will  have  an 
acceleration  in  a  vertical  direction  due  to 
harmonic  motion  while  that  of  the  cross- 
head  end  will  differ  from  this  because  of 
the  angularity  of  the  connecting  rod.  In 
Fig.  ST,  AD  =  s  =  space  passed  over  by  rotating  parts  in 
tical  direction  in  time  t.     Angular  velocity  =  a. 

s  =  r  —  r  cos  at, 

velocitv  =  v-z  =  —  =  ar  sin  at, 
at 

acceleration  =  U  =  -r-  =  a-r  cos  at. 
dt^ 


a  ver- 


(58) 


Io8     THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


In  the  case  of  the  crosshead: 

FE  =  s  =  space  passed  over  by  reciprocating  parts  in  a 
vertical  direction  in  time  t. 
s  =  FA  +  AO  -  OD  -  ED  ^  I  +  r  -  r  cos  at  -  V/2  -  r^  sin^  at 


=  r(i-\-  -  —  cos  at  —  y 


ds 
'l}i=—  =  ar  sin  at 
dt 


1  + 


ty 

cos  at 


Sin^  at 


/l 


d^ 
df" 


a'r 


cos  at  4- 


cos  2  at 


sin^  2  at 


N/e;- 


sin^  at     4 


—  sin-  a/ 


(59) 


It  is  customary  to  neglect  the  last  term  of  this  expression  since 

its  maximum  value  when  -  =  4  is  0.004,  and  the  denominator 

r 

of  the  preceding  term  is  also  simplified  by  dropping  the  shi^  at. 
The  approximate  expression  for/i  then  becomes 

/i  =  aV  I  cos  at+  -  cos  2  at\ . 

ar  =  linear  velocity  of  crank  pin  =  v. 

f\=  —{  cos  at-\-    -  COS  2  at\.  (60) 

If  M  =  mass  of  the  reciprocating  parts  the  accelerating  force 


IS 


t  =  I  COS  at-\-  -  COS  2  at 


) 


(61) 


Another  form  in  which  this  accelerating  force  can  be  expressed 
is  as  follows: 

F  =  - — 
r 


cos  at 
+  COS  2  at 

+  COS  4  at 


I^ 


L/+H/;+7Sl/'  + 


ilD+^g- 


+  COS  6  a/  [ 

etc. 


•  (62) 


ENGINE  BALANCING 


109 


Approximately, 

F  =  M—  cos  at 
r 

(A) 

y2     f. 

-j-  M—  -  cos  2  at 

r  I 

(B) 

+  M 7     cos  4 

r  4\IJ 

at. 

(C) 

etc. 

(63) 


Since 


V  =  2  irrn.  '  j 
(A)  =  M  4  irnh  cos  a/. 

(5)   =  M  4  7r2  (2  w)2  —  COS  2  a/. 

4/ 

(C)  =  M  4. 7r2  (4  w)2  — --  COS  4  a/. 


64/3 


etc. 


These  last  three  expressions  can  be  represented  graphically  as 


shown  in  Fig.  58. 

Let        r  =  radius  of  crank  =  i. 
1  =  4. 

M  is  the  mass  of  the  piston,  piston 
rod,  crosshead,  slipper,  and  upper  end 
of  the  connecting  rod. 

125.  Primary  and  Secondary 
Masses.  —  The  mass  M  rotating  with 
an  angular  velocity  a  on  a  radius  r  =  i 
would  give  rise  to  a  force  whose  ver- 
tical component  is  called  the  primary 
hammering  force.     The  mass  M  ro- 


1  _ 


Ml^ 


tating  on  a  radius 


4/ 


— ,  with  an 
16 


Fig.  58. 


angular  velocity  2  a,  gives  rise  to  a  force  whose  vertical  compo- 
nent is  called  the  secondary  hammering  force.  These  are  the 
only  two  forces  usually  considered,  but  if  a  nearer  approximation 

were  desired  we  could  add  a  third  mass  M  rotating  on  a  radius 
4 

with  an  angular  velocity  4  a. 


r 


4096 


no       THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

126.  Approximations.  —  We  have  made,  then,  two  principal 
approximations:  first,  that  the  length  of  the  connecting  rod  is 
infinite  and  that  its  mass  can  be  divided  into  two  fixed  portions, 
one  acting  at  the  crosshead  and  the  other  at  the  crank  pin; 
second,  that  the  effect  of  the  reciprocating  masses  is  essentially 
the  same  as  if  we  were  dealing  with  the  vertical  components  of 
the  centrifugal  forces  arising  from  the  rotation  of  two  masses, 
each  equal  to  the  reciprocating  masses,  —  one  making  the  same 
number  of  revolutions  as  the  main  engine  on  a  radius  r,  the  other 

revolving  twice  as  fast  on  a  radius  — -• 

4I 

127.  Valve  Gear  Treated  as  Rotating  Mass.  —  It  will  be  seen 
that  the  expression  for  the  secondary  force  contains  the  expression 

— ,  so  that  when  the  ratio  o(l  tor  is  large  the  value  of  the  second- 
4I 

ary  force  is  small.     In  the  case  of  the  valve  gear  the  length  of  the 

eccentric  rod  is  usually  from  20  to  30  times  the  eccentricity,  so 

that  we  can  neglect  the  secondary  forces  without  any  great  error 

in  this  case.     This  makes  the  disturbance  due  to  the  valve  gear 

equivalent  to  the  vertical  component  of  the  centrifugal  force 

arising  from  the  uniform  rotation  of  a  mass  equal  to  the  mass  of 

the  valve  gear.     If  we  balance  this  with  a  rotating  mass  we  shall 

have  overbalance  in  a  horizontal  direction  since  the  valve  gear 

has  motion  only  in  a  vertical  direction. 

It  is  customary  to  find  the  resultant  effect  of  all  the  valve  gears 
and  then  balance  this  resultant  with  a  rotating  mass.  In  the 
case  of  the  M.P.  cylinder  or  cylinders  it  is  possible  to  have  the 
valves  take  steam  on  the  inside  or  on  the  outside  and  the  re- 
sultant unbalanced  force  may  be  reduced  by  changing  the  angle 
of  the  eccentrics  to  suit  one  method  or  the  other.  The  engine 
is  balanced  for  the  go-ahead  position  with  the  ahead  eccentric 
actuating  the  valve,  valve  stem,  crosshead,  half  the  drag  rods, 
half  the  Hnk,  one  eccentric  rod,  and  one  strap.  The  backing 
eccentric  actuates  half  the  hnk,  one  eccentric  rod,  and  one  strap. 
The  resultant  for  the  valve  gears  can  be  found  by  the  method 
shown  in  Figs.  52,  53,  and  54. 

By   means    of    these    assumptions    and    approximations    the 


ENGINE  BALANCING 


III 


question  of  engine  balancing  is  reduced  to  the  consideration  of 
three  revolving  masses  for  each  cylinder.  One  of  these  is  the 
sum  of  the  masses  which  are  supposed  to  have  a  motion  of  rota- 
tion; namely,  the  unbalanced  portions  of  the  crank  webs,  crank 
pins,  lower  part  of  connecting  rod,  eccentrics,  eccentric  straps, 
eccentric  rods,  links,  link  blocks,  valve  stems,  and  valves,  all 
reduced  to  equivalent  masses  acting  at  the  crank  pin  and  rotating 
at  the  same  number  of  revolutions  as  the  main  engine.  Another 
of  these  masses,  called  the  primary  mass,  is  the  sum  of  those 
which  are  supposed  to  reciprocate  and  is  made  up  of  the  upper 
part  of  the  connecting  rod,  crosshead,  slipper,  piston  rod,  and 
piston,  all  rotating  with  the  same  number  of  revolutions  as  the 
main  engine,  upon  a  radius  equal  to  the  length  of  the  crank  arm. 
The  third  mass  is  called  the  secondary  mass,  and  is  equal  to  the 
primary  mass,  but  is  rotating  with  twice  the  number  of  revolu- 
tions of  the  main  engine,  upon  a  radius  equal  to^ — ,• 

4/ 

128.  Balance  with  Bob  Weights.  —  The  reciprocating  masses 
are  not  as  easily  balanced  as  the  rotating,  by  reason  of  the  fact 
that  we  have  to  deal  with  the  secondary  masses.  The  primary 
masses  might  be  balanced  by  a  bob  weight  actuated  by  a  crank 
making  the  same  number  of  revolutions  as  the  main  engine.  The 
secondary  masses  would  have  to  be  balanced  by  a  bob  weight 
actuated  by  a  crank  making  twice  as  many  revolutions  as  the 
main  engine,  and  this  would  necessitate  the  introduction  of  gear- 
ing which  is  usually  not  practicable.  If  bob  weights  are  to  be 
used  we  would  proceed  in  the  same  manner  as  for  the  balance  of 
rotating  masses:  select  the  planes  in  which  the  bob  weights  are 
to  act,  find  the  components  which  are  to  act  in  those  planes,  and 
combine  the  components  at  the  proper  angle  with  one  another  to 
find  the  resultant  weight  and  the  angle  at  which  the  actuating 
crank  is  to  be  set. 

129.  Balance  without  Use  of  Extra  Weights.  —  It  is  usual, 
however,  to  avoid  the  use  of  any  extra  cranks  and  bob  weights, 
and  to  arrange  the  crank  angles,  relative  location  of  cylinders, 
and  weights  of  the  reciprocating  parts  so  as  to  secure  as  nearly 
as  possible  perfect  balance.     If  we  have  a  force  diagram  such  as 


112      THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


is  shown  in  broken  lines  in  Fig.  59  for  the  primary  forces  of  a 
four-cylinder  engine  we  should  need  a  force  Od  to  close  the  dia- 
gram, but  if  we  arrange  the  crank  angles  differently  and  perhaps 
increase  or  decrease  some  of  the  reciprocating  masses  we  can  get 
the  diagram  to  close  as  shown  in  the  full  lines  of  Fig.  59.  It 
might  be  thought  that  since  we  are  in  reality  concerned  only 
with   the   vertical   components    of   these   forces,   if   we   had   a 


Fig.  59. 

condition  such  as  is  shown  by  Fig.  60  the  engine  would  be 
balanced.  The  engine  would  be  balanced  for  that  crank  position 
but  as  soon  as  the  cranks  revolve  slightly  the  balance  would  be 
destroyed.  In  order  that  the  arrangement  of  cranks  and  weights 
shall  be  such  as  to  be  balanced  in  all  positions  it  is  necessary  that 
the  sum  of  both  the  horizontal  and  vertical  components  of  the 
forces  shall  equal  zero. 

130.  Equations  for  Force  and  Moment  Diagrams.  —  The 
determination  of  the  conditions  for  perfect  balance  will  involve 
the  use  of  two  equations  for  each  force  or  moment  diagram.  We 
shall  have  one  force  diagram  for  the  primary  hammering  forces, 
another  for  the  secondary  hammering  forces,  one  moment  diagram 
for  the  primary  tilting  couples,  and  another  for  the  secondary 
tilting  couples.  In  all  we  shall  have  to  deal  with  eight  equations, 
each  equation  involving  as  many  terms  as  there  are  cranks. 

Primary  forces  disappear  if 

(i)     -  {Ml  cos  ^  -f  M2  cos  5  +  M3  cos  C  +  •  •  •  )  =  o. 
r 

(2)    -  {Ml  sin  ^  +  M2  sin  ^  +  M3  sin  C  +  •  •  •  )  =  o. 


ENGINE   BALANCING 


113 


Primary  couples  disappear  if 

(3)  -  {Miai  cos  A  +  Moo-i  cos  B  +  if  303  cos  C  +•••)=  o- 
r 

(4)  -  (MiOi  sin  A  +  Mao^  sin  B  +  If 303  sin  C  +  •  •  •  )  =  o. 
r 

Secondary  forces  disappear  if 

(5)  -  -  (Ml  cos  2  yd  +  if2  cos  2  5  +  Afs  cos  2  C  +  •  •  • )  =0. 
/  r 

(6)  7  -  (Ml  sin  2  ^  +  Mo  sin  2  i5  +  M3  sin  2  C+  •  •  •  )  =0. 


Fig.  61. 


Secondary  couples  disappear  if 


r  V' 


(7)     :  '-  (Miflicos  2  A  -\-M2a2  cos  2  B+M^as  cos  2  C+ 
/   r 


r  V- 


(8)    -  -  (MiGTi  sin  2  A  +  Moai  sin  2  5+M3fl3  sin  2  C+ 


)=o. 
)  =  o. 


V  =  linear  velocity  of  crank  pin. 
r  =  radius  of  crank-pin  circle. 
/  =  length  of  connecting  rod  between  centers. 
Ml,  M2,  M3,  etc.  =  masses  of  reciprocating  parts  of  different 
cylinders. 
di,  (12,  dz,  etc.  =  distance  of  different  cylinders  from  ref- 
erence plane. 
A,  B,  C,  etc.  =  angles  that  cranks  make  vnth  reference 
line  (see  Fig.  61). 


114     THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

131.  Order  in  which  Equations  Must  be  Used.  —  It  is  obvious 
that  the  equations  must  be  taken  in  pairs  since  satisfying  equa- 
tion (i)  but  not  (2)  would  mean  that  for  one  particular  position 
of  the  cranks  the  sum  of  the  vertical  components  equals  zero, 
but  if  the  cranks  are  revolved  sHghtly  equation  (i)  will  not  equal 
zero. 

In  the  above  equations  we  have  the  quantities  ai,  Oo,  fls,  etc., 
which  are  the  distances  from  some  chosen  reference  plane  to  the 
planes  in  which  the  reciprocating  masses  are  acting.  It  is 
possible  that  we  may  so  choose  the  location  of  our  reference 
plane  that  equations  (3),  (4),  (7),  and  (8)  will  be  satisfied,  but  if  a 
new  reference  plane  is  used  these  equations  may  not  be  satisfied. 
If  the  engine  is  "perfectly"  balanced  the  moment  diagrams  ought 
to  close  no  matter  where  the  reference  plane  is  taken. 

In  Fig.  61  let  the  reference  plane  be  moved  a  distance  z. 
Equation  (3)  will  then  become 

-  [Ml  (fli  +  z)  cos  A  +  Ml  {do  +  z)  cos  B  -\-  Mz  (03  +  z)  cos  C 
r 

+   ...]=  o, 

or, 

—  [{MiQi  cos  A  -f  71/202  cos  B  +  MsQs  cos  C  +  .  .  .  ) 
r 

-f  z  (Ml  cos  ^  +  1/2  cos  -6  +  M3  cos  C  +   .  .  .  )]  =  o. 

This  is  equation  (3)  with  the  expression  z  (Mi  cos  A  +  M2 
cos  B  +  Mz  cos  C)  added,  and  will  still  be  equal  to  zero  if  the 
quantity  (Mi  cos  A  +  Mo  cos  B  +  M3  cos  C)  is  equal  to  zero. 
This  latter  expression  is  the  same  as  equation  (i).  In  other 
words,  we  must  satisfy  equations  (i)  and  (2)  before  we  satisfy 
(3)  and  (4)  and  must  satisfy  (5)  and  (6)  before  satisfying  (7)  and 
(8).  Not  only  must  the  equations  be  taken  in  pairs  but  they 
must  be  taken  in  a  certain  sequence.  If  we  have  enough  un- 
knowns to  satisfy  only  two  equations  we  could  choose  (i)  and 
(2),  or  (5)  and  (6),  but  since  the  primary  forces  are  much  larger 
than  the  secondary,  we  would  naturally  choose  (i)  and  (2).  If 
there  are  enough  unknowns  for  four  equations  we  can  satisfy  (i), 
(2),  (3),  and  (4),  or  (i),  (2),  (5),  and  (6).     It  would  of  course 


ENGINE   BALANCING  1 15 

be  possible  to  satisfy  (5),  (6),  (7),  and  (8),  but  it  would  not  be 
wise  to  eliminate  the  lesser  forces  instead  of  the  greater.  If  six 
equations  could  be  satisfied  the  choice  would  probably  be  (i), 
(2),  (3),  (4),  (5),  and  (6). 

132.  Number  of  Unknown  Quantities.  —  The  number  of 
unknowns  in  any  case  will  be  a  function  of  the  number  of  cranks. 
In  order  that  we  ma}'  be  able  to  make  use  of  the  results  obtained 
from  our  force  and  moment  diagrams  we  must  know  one  mass 
and  the  distance  of  that  mass  from  our  reference  plane.  If  n  is 
the  number  of  cranks,  the  greatest  possible  number  of  unknown 
masses  M  will  be  {n  —  i),  and  the  unknown  arms  a  can  also  be 
as  great  as  (n  —  i).  The  greatest  possible  number  of  unknown 
angles  between  the  cranks  will  be  {n  —  i).  Therefore  the 
greatest  number  of  unknown   quantities  in  any  case  will  be 

3  (n  -  i)- 

133.  Single-crank  engine.  —  In  this  case  3  (i  —  i)  =  o. 
None  of  the  equations  can  be  satisfied,  so  the  reciprocating  parts 
cannot  be  balanced.  The  rotating  parts  can  be  balanced  by 
other  rotating  weights. 

134.  Two-crank  engine.  —  In  this  case  the  greatest  number 
of  unknowns  can  be  3  (2  —  i)  =  3.  Since  the  equations  have 
to  be  taken  in  pairs  we  can  satisfy  only  two,  and  the  equations 
chosen  will  probably  be  (i)  and  (2). 

—  (Ml  cos  A  -\-  M-z  cos  B)  =  o. 
r 

—  (Ml  sin  A  -\r  Ml  sin  B)  =  o. 

Let  Ml  be  known,  and  the  position  of  the  cranks  such  that 

A  =o\ 

—  (Ml  +  Mo  cos  B)  =  o. 
r 

—  (M9  sin  B)  =  o. 
r 

M2  cannot  =  o,  .'.  sin  B  =  o,  and  B  must  =  0°  or  180°.  If 
B  =  0°,  we  have  a  one-crank  engine.  .".  B  must  =  180°.  If 
B  =  180°,  Ml  =  M2.     We  have  as  a  result  of  these  conditions 


Il6     THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


two  cylinders  in  the  same  plane,  the  reciprocating  masses  equal 
and  actuated  by  cranks  at  i8o°.  Tliis  gives  the  arrangement 
recommended  by  McAlpine.     (See  Fig.  62.) 

135.  Three-crank  Engine.  —  The  greatest  number  of  un- 
knowns for  this  engine  will  be  3  (3  —  i)  =  6.  When  the  first 
six  equations  are  solved  the  following  relations  are  obtained: 

Ml  =  M2  =  M3. 
cos  B  =  cos  C  =  —  |.  * 

sin  B  =  —  sin  C. 
a\  =  ai  =  C3. 

This  gives  an  engine  with  the  reciprocating  masses  of  the  three 
cylinders  all  equal ;  the  cranks  at  1 20°,  and  all  in  the  same  plane 


Fig.  62. 


Fig.  63. 


(see  Fig.  63).  This  arrangement  is  of  no  practical  use.  If  we 
give  02  and  03  such  values  as  will  separate  the  cylinders  we  shall 
still  have  four  unknowns  and  can  satisfy  the  first  four  equations. 
The  results  of  this  solution  are  as  follows: 

Ml  +  M^  =  Ml. 
MiCh  —  MzQz  =  o. 

cos  B  =  —1. 
cos  C  =  +1. 


ENGINE   BALANCING 


117 


This  gives  the  arrangement  shown  in  Yig.  64;  one  heavy 
set  of  reciprocating  masses  between  two  lighter  sets  and  making 
an  angle  of  180°  with  them.  It  is  not  desirable  to  have  the  cranks 
at  180°  on  account  of  the 
great  variation  in  turning 
moments  which  results 
from  this  arrangement. 
Engines  are  sometimes 
made  with  the  low-pres- 
sure cy Under  in  the  middle 
but  with    the   cranks    at 

o 

120  . 

136.   Four-crank      En- 
gine. —  The     total     un- 
knowns with  this  number  ^^^-  ^4- 
of  cranks  can  be  3  (4  —  i)  =  9.     As  there  are  only  eight  equa- 
tions to  solve  we  will  let  a-2  be  a  known  quantity  as  well  as  ai. 
When  the  eight  equations  are  solved  we  find  that  the  follo^^^ng 

conditions  must    exist  for 


'perfect"  balance: 


M2  =  M3. 

Mi  +  Ml  =  Mo  =  M3 

1/4^4  =  Moo^- 

as  =  (h- 
sin  C  =  —sin  B. 
cos  C 

cos  Z)  =  I . 
sin  D  =  o. 


cos  B  =  — §. 


Fig.  6.^ 


This  results  in  the  ar- 
rangement shown  in  Fig. 
65,  an  arrangement  which  is  not  possible  since  it  brings  two 
cylinders  in  the  same  transverse  plane.  If  we  increase  our 
known  quantities  by  two  and  reduce  our  unknowns  to  six  we 
can  satisfy  the  first  six  equations  and  get  a  possible  solution. 

137.   Yarrow-Schlick-Tweedy  System.  —  The  two  additional 
known  conditions  can  be  so  chosen  that  we  get  an  engine  vnth  a 


Il8      THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

symmetrical  arrangement  of  cylinders.  This  arrangement  is 
commonly  known  as  the  Yarrow- SchHck-T weedy  system  of 
balancing.  We  will  use  the  notation  common  to  this  system, 
see  Fig.  66,  in  which  a  is  the  angle  between  cranks  i  and  4,  7  is 
the  angle  between  cranks  2  and  3,  /3  is  the  angle  between  cranks 
I  and  3,  and  /3i  is  the  angle  between  cranks  2  and  4. 


Fig.  66. 

Ml  and  ai  must  be  known  anyway  and  the  three  additional 
known  conditions  will  be  as  follows: 


Let 


Gi  —  —a\. 

^2    =     —  ^3. 

M4    =   My. 


This  gives  the  symmetrical  arrangement  shown  in  Fig.  66. 
When  the  first  six  equations  are  solved  we  have  the  following 
results: 


M2 

= 

Mz 

iS 

= 

^1. 

MyL 

.     a 

sm  - 
2 

= 

Mai 

a 
cos- 

2 

T 
cos  — 

2 

= 

I 
2 

L  tan  -  =  I  tan  -• 


Mz  cos  -  =  Ml  cos  -. 


ENGINE  BALANCING  119 

On  account  of  the  symmetry  of  the  arrangement  we  can  reduce 
the  actual  unknown  relations  to  three,  as  follows: 

if 3  cos-  =  Ml  cos- •  (64) 


005^^-=^  =  -+h-\Jlfi+^-  (65) 


y  -  cc  _l  _  /.  ,  i/A2  1  3 


cos^^ =  --//  +  \h^  +  ^-  (66) 

22  *  4 

This  is  the  system  of  balancing  most  commonly  used  and  the 
more  nearly  the  value  of  —  approaches  unity  the  more  nearly 
the  angles  a  and  7  approach  90°.  It  is  difficult,  however,  to  get 
the  value  of  —  to  exceed  0.5   without  lengthening  the  engine 

considerably. 

138.  Unsymmetrical  Four-crank  Arrangement.  —  In  addition 
to  the  above  symmetrical  arrangements  there  are  an  infinite  num- 
ber of  unsymmetrical  arrangements  of  cylinders,  crank  angles, 
and  reciprocating  weights  which  will  give  an  engine  balanced  for 
primary  forces,  secondary  forces,  and  primary  tilting  couples. 

Mr.  Chas.  E.  Inglis,  M.  A.,  in  a  paper  read  before  the  Institute 
of  Naval  Architects  in  191 1,  gives  certain  diagrams  which  greatly 
reduce  the  labor  involved  in  selecting  the  proper  relations  for 
balance.  Usually  the  relative  location  of  cylinders  will  be  quite 
closely  determined.  There  are  certain  practical  limits  set  upon 
the  maximum  length  of  an  engine,  and  the  sizes  of  the  different 
cylinders  and  valve  chests,  and  the  sizes  of  the  crank-shaft  parts 
will  determine  the  minimum  distance  between  cylinder  centers. 
Fig.  67,  which  is  taken  from  the  above-mentioned  paper,  is  so 
drawn  that  if  the  relative  location  of  the  cylinders  is  known  the 
crank  angles  which  will  give  freedom  from  primary  tilting  couples 
can  be  determined.  These  angles  should  satisfy  the  following 
equation : 

2  cos  -  cos  -  =  cos (68) 

222 


I20     THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

In  order  that  freedom  from  primary  and  secondary  hammering 
may  be  obtained  the  following  relation  between  masses  and 
crank  angles  should  exist: 


15  20 


0  12        3         4         6  6         7 


10       11       12       13       U      15       16        17       18       19        20 


Fig.  67. 


M2  =  Mo 


.    d    .     /     ,5 

sm  a  sin  -  sm   a-j-  - 

2        \        2 


sm  j8  sin  -  sin 

2 


M 


sm  a  sm  | )  sm 


Ms  =  Mo 


M 


Ml  =  Mo 


sin  (/3  +  7)  sin  (i3  +  -  j  sin  - 

(^1 


sm  8  sm sm 


sin  (/3  +  7)  sinf  7  +  - 1  sin 


(69) 


(70) 


(71) 


Mq  can  be  taken  as  unity,  in  which  case  the  equations  will  give 
the  relative  weights  of  the  masses. 

The  disturbance  due  to  the  secondary  tilting  couples  can  be 
determined  by  introducing  the  above  distances,  angles,  and 
masses  into  equations  (7)  and  (8). 


ENGINE   BALANCING 


121 


The  significance  of  Fig.  67  can  be  shown  by  the  following  proof. 
In  Fig.  68  let  ce  represent  by  its  length  the  mass  of  Mi  in  Fig.  69, 
and  let  its  direction  be 
parallel  to  the  crank  arm 
of  Ml.  In  the  same  way 
let  ea  represent  M3,  ag 
represent  M2,  and  gc  rep- 
resent M4.  Since  these 
four  lines  make  a  closed 
diagram  the  resultant  of 
the  primary  hammering 
forces  is  zero  and  we  can 
investigate  the  primary 
tilting  couples.  If  we 
take  our  plane  of  refer- 
ence through  Ml  the  poly- 
gon of  primary  tilting  couples  will  be  a  triangle,  such  as  eja  in 
Fig.  68.  Draw  dej  parallel  to  ag,  aj  parallel  to  eg,  and  eh  parallel 
to  eg.     If  the  resultant  of  the  primary. til  ting  couples  is  to  be  zero 


Fig.  69. 


Mi(h,  Mzdi,  and  MiOi  must  have  such  values  that  they  can  be 
represented  by  ef,  ea,  and  af. 


then 


Moo-i  :  MzGz  :  M4(74 
Midi 


cf  :ea  :  af, 

'1- 

af 


122      THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


but 


also, 


Ma      ag      df 
Mi      cg~af' 
MzQz      ae 


Ga      af      df     df      ad ' 


but 


«3 


ae 


M^a^  af 
Mz  _  ae 
Mi~  eg' 

This  proves  that  the  resultant  of  the  primary  tilting  couples 
wiU  be  zero  if  0-2  :  as  :  a^  =  ab  :  ac  :  ad.     The  point  e  of  any  such 


ai      af      ae      af      ad 


Fig.  70. 

diagram  as  shown  in  Fig.  68  can  be  obtained  from  Fig.  67  by 
finding  the  intersection  of  the  curves  corresponding  to  points  b 
and  c. 


M4&M1 


.^ 


Mj&Ms     ^''^°"        M. 


Fig.  71. 


139.  Engines  with  Five  or  more  Cranks.  —  The  arrangement 
which  will  give  balance  in  engines  with  five  or  more  cranks  can 
be  determined  by  combining  two  or  more  groups  of  "perfectly" 
balanced  four-crank  engines.  In  Fig.  71  we  see  how  the  two 
sets  of  four-crank  engines  shown  in  Fig.  70  can  be  combined  to 


ENGINE   BALANCING 


123 


give  a  five-crank  engine.  The  two  sets  of  four-crank  engines  are 
identical  except  that  the  distance  between  the  outside  cylinders 
is  greater  in  one  case  than  in  the  other.  If  one  engine  is  imposed 
upon  the  other  so  that  M^,  M3,  and  M2,  Mz  are  in  the  same  plane 
we  shall  have  three  masses  in  this  plane  which  fulfill  the  require- 
ments for  a  "perfectly"  balanced  three-crank  engine  (see  Fig. 
63) ;  i.e.,  the  three  masses  are  equal  and  the  cranks  make  angles  of 
120°.  This  balanced  set  of  three  cranks  can  be  eliminated  and 
the  remaining  five  cranks  will  be  in  ''perfect"  balance.  The 
conditions  will  be  as  follows: 

Ml  -f  M4  =  Mi  +  Mz  =  M5. 

MiGi  =  M^di. 

MzQz  =  M^ch- 

Ml  and  M^  are  in  the  same  axial  plane. 
M2  and  Mz  are  in  the  same  axial  plane. 
Cranks  are  in  planes  making  120°. 

In  the  same  way  three  sets  of  "perfectly"  balanced  four-crank 
engines  can  be  combined  to  give  a  six-crank  engine  after  the 


5^ 


M,&IVIe   ^120"    IVI3&M4 


Fig.  72. 


eHmination  of  two  sets  of  balanced  three-crank  engines.  Fig.  72 
shows  the  resulting  arrangement  for  the  six-crank  engine.  The 
conditions  will  be  as  follows: 

Ml  ^-  M2  =  M3  -F  M4  =  Ms  -f  Me. 

MiOi  =  Mia-i. 

MzQz  =  M^a^. 

M^a^  =  Mefle- 


124      THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

Ml  and  M2  are  in  the  same  axial  plane. 
Mz  and  Mi  are  in  the  same  axial  plane. 
Ms  and  M^  are  in  the  same  axial  plane. 
The  axial  planes  make  angles  of  120°. 

140.  Summary.  — •  In  the  case  of  three-crank  engines  the  in- 
vestigation shows  that  the  primary  and  secondary  hammering 
forces  can  be  balanced  if  the  heaviest  cylinder  is  placed  in  the 
middle  of  the  engine  and  the  cranks  are  180°  apart.  The  nearest 
approach  to  this  in  practice  is  to  place  the  L.P.  cylinder  between 
the  H.P.  and  the  M.P.,  but  the  cranks  are  placed  120°  apart  to 
keep  the  turning  moment  more  nearly  constant. 

Four-crank  engines  can  be  balanced  for  primary  and  secondary 
hammering  forces  and  for  the  primary  tilting  couples.  The 
most  common  form  in  practice  is  that  used  in  the  case  of  four- 
cylinder  Triples,  where  the  L.P.  cylinders  are  placed  on  the  ends 
of  the  engine  with  the  H.P.  and  M.P.  between  them. 

Five-  and  six-crank  engines  can  be  balanced  for  primary  and 
secondary  hammering  forces  and  primary  and  secondary  tilting 
couples.  Five-crank  engines  are  seldom  built,  and  six-crank 
engines  are  rarely  found  except  in  small  speed  boats  and  auto- 
mobiles. Even  in  five-  and  six-crank  engines,  however,  the 
balance  is  not  absolutely  perfect  because  of  the  assumptions 
made  regarding  the  connecting  rod  and  because  of  the  simphfied 
expression  used  for  the  acceleration  of  the  crosshead. 


SECTION  IV 
CONDENSERS  AND  AIR  PUMPS 

141.  Partial  Pressures.  —  Before  taking  up  the  effect  of  air 
upon  condensation,  attention  must  be  directed  to  Dalton's  law 
of  partial  pressure  for  mixed  gases.  If  two  gases,  such  as  air 
and  water  vapor,  are  mixed  in  a  receptacle,  the  total  pressure 
exerted  is  the  sum  of  the  pressures  that  each  gas  would  exert  if 
the  same  weight  of  gas  which  is  present  in  the  mixture  occupied 
the  entire  volume  of  the  receptacle  alone.  Thus,  if  we  should 
take  I  cubic  foot  of  saturated  water  vapor  at  102°  F.  and  force  it 
into  a  receptacle  containing  a  cubic  foot  of  air  at  102°  F.  and  at 
a  pressure  of  o.  i  pound  absolute,  the  total  pressure  of  the  cubic 
foot  of  mixture  would  be  i.i  pounds  since  water  vapor  at  102°  F. 
has  a  pressure  of  i  pound  absolute.  This  is  true  only,  however, 
when  we  have  an  equilibrium  of  temperature.  If  we  should  take 
a  cubic  foot  of  steam  at  120°  F.  and  add  it  to  a  cubic  foot  of  air 
at  70°  F.  and  o.  i  pound  absolute  the  total  pressure  would  de- 
pend upon  the  final  temperature  assumed  by  the  mixture  of 
steam,  water,  and  air. 

142.  Efifect  of  Air  upon  Rate  of  Condensation.  —  A  paper 
was  read  before  the  Victorian  Institute  of  Engineers  on  Dec.  6, 
1905,  by  James  Alexander  Smith,  in  which  the  effect  of  air  upon 
surface  condensation  was  discussed.  The  experiments  were 
made  upon  a  small  scale  and  under  conditions  differing  some- 
what from  those  existing  in  surface  condensers  as  ordinarily 
used.  The  experiments  were  conducted  by  means  of  a  cylinder 
7^  inches  in  diameter  and  3  feet  long.  Two  f-inch  tubes  3  feet 
long,  connected  in  series,  ran  through  the  condenser  and  carried 
the  cooling  water.  Burners  were  placed  under  the  tank  and 
were  used  to  generate  steam  and  keep  the  conditions  uniform 
while  condensation  took  place  on  the  surface  of  the  tubes.  The 
receptacle  served  as  boiler  and  condenser  combined.     The  ex- 

125 


126     THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


perimental  results  are  valuable,  however,  as  they  show  very 
clearly  the  injurious  effect  of  air  in  condensers.  Fig.  73,  taken 
from  this  paper,  shows  the  effect  of  different  air  mixtures  upon 
the  rate  of  heat  transmission.  When  the  partial  pressure  of  the 
air  is  zero  we  are  deahng  with  saturated  steam  and  it  will  be 


300 

\-0 

\  V 

r. 

250 

^  V 

^  '  \ 

200 

Q. 
u. 

CO 

1\ 

\, 

k-5^ 

\^ 

\, 

V,: 

^^ 

^0 

150 

l\ 

\ 

S-? 

.^ 

■  '■'0° 

-^ 

£io 

5" 

UJ 
Q. 

\ 



ipj- 

r- 

— 

. 

100 

D 

\l 

s 

^ 

-i?0° 



?6.5P^ 



1- 

\. 

^ 

^ 

"■~~~" 

^ 

2L1 

r- 

<-.5 

N^ 

^ 

■ — 

200, 
90°- 

-*— « 

- 

2R' 

■ — 1 

50 

^^ 

Pn 

^ 

■•»^; 

^ 

r- 

28.5 

"— ~ 

, 8p^_ 

28t9" 1 

0      .1      ,2     .3 


A     .5     .6     .7      ,8      .9     1,0    1,1     1.2    1,3    1.4   1,5    1,6    1,7    1.8    1.9   2.0 
Partial  Press.of  Air (7.'o°f.)Ins.of  Mercury 
,  Temp.X°_ 


Pressure  at  X°= 


531 

Fig.  73. 


-Press,  at  70° 


noticed  that  a  small  addition  of  air  causes  a  rapid  decrease  in  the 
rate  of  condensation  especially  at  high  vacua.  A  partial  air 
pressure  of  0.2  inch  at  a  vapor  temperature  of  80°  F.  causes 
the  efficiency  of  the  surface  to  be  decreased  by  more  than  50  per 
cent.  The  same  partial  pressure  at  a  vapor  temperature  of 
140°  F.  causes  a  smaller  loss  of  about  27  per  cent  in  surface 
efficiency,  although  the  decrease  in  B.t.u.  transmitted  is  larger 
than  in  the  first  case. 

In  the  experimental  condenser  all  the  temperatures  of  vapor, 
air,  and  water  were  in  equilibrium  and  the  air  was  uniformly 
distributed  throughout  the  condenser.  In  actual  practice  we  do 
not  have  this  equilibrium.     In  the  steam  entering  the  top  of  the 


CONDENSERS   AND   AIR   PUMPS  127 

condenser  the  proportion  of  air  is  so  small  that  the  steam  is 
practically  saturated  and  the  temperature  is  that  corresponding 
to  the  pressure  of  saturated  steam.  As  the  mixture  of  steam  and 
air  passes  between  the  tubes  the  steam  is  condensed  and  the  pro- 
portion of  steam  to  air  becomes  less  so  that  the  partial  pres- 
sure of  the  air  increases  and  the  temperature  falls.  We  have, 
then,  practically  saturated  steam  at  the  top  of  the  condenser 
and  almost  pure  air  at  the  bottom  with  a  varying  mixture  in 
between.  There  is  probably  a  tendency  for  the  air  to  accumu- 
late around  the  tubes,  since  there  is  a  movement  of  the  steam 
towards  the  cooling  surface  where  it  is  condensed,  lea\'ing  the  air 
uncondensed.  The  velocity  of  steam  and  air  passing  over  the 
tubes  will  prevent  this  accumulation  of  air  to  any  great  extent. 
The  time  taken  by  the  steam  and  air  to  pass  through  the  con- 
denser is  only  a  part  of  a  second  due  to  the  fact  that  the  velocity 
between  the  tubes  is  usually  from  100  to  200  feet  per  second  at 
the  top,  and  about  20  feet  per  second  in  the  pipe  leading  to  the 
air  pump. 

By  reason  of  this  variation  in  the  temperature  of  the  mixture 
as  it  passes  through  the  condenser,  the  rate  of  heat  transmission 
would  not  follow  any  one  of  the  isothermals  shown  in  Fig.  73 
but  would  be  a  steeper  curve,  such  as  AB,  cutting  across  the 
isothermals. 

It  should  be  noticed  in  Fig.  73  that  the  partial  pressures  are 
given  for  air  at  70°  F.  If  it  is  desired  to  find  the  pressure  of  the 
mixture  of  air  and  vapor  which  would  transmit  50  B.t.u.  per 
square  foot  per  minute  at  a  temperature  of  90°,  we  should  take 
the  partial  pressure  of  the  steam,  1.5  inches  of  mercury,  and  add 

to  it  0.24  X  ^^-  =  0.249  inch. 
531 

The  total  pressure  would  then  be  1.5  +  0.249  =  i-749  inches 
mercury,  or  about  0.875  pound  absolute. 

The  effect  of  air  upon  the  rate  of  temperature  increase  of  water 
passing  through  the  condenser  tube  is  shown  by  the  curves  of 
Fig.  74.  Curves  A  and  B  are  from  Mr.  Smith's  experiments,  A 
is  for  saturated  steam  and  B  is  for  a  mixture  of  steam  and  air 
of  such  proportion  that  the  partial  air  pressure  is  0.22  inch  of 


128      THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


mercury.  In  the  experimental  condenser  everything  was  in 
equilibrium  and  there  was  no  movement  of  the  steam  except  as 
new  steam  was  generated  to  take  the  place  of  the  steam  con- 
densed. It  is  probable  that  there  was  a  tendency  for  the  air  to 
accumulate  around  the  tubes.     The  other  curves  in  Fig.  74  are 


4  8  12 

Travel  of  Water  in  Feet 

Fig.  74. 


16 


from  the  experiments  made  by  Professor  Weighton  upon  a 
Contrafio  condenser,  one  group  of  three  curves  being  for  a  rate 
of  condensation  of  about  19.5  pounds  of  steam  per  square  foot 
of  cooling  surface  per  hour,  and  the  other  group  for  about  8.75 
pounds  per  hour.  It  has  been  pointed  out  before  that  condens- 
ers in  ordinary  use  have  practically  pure  saturated  steam  at  the 
top,  and  at  the  bottom  air  with  a  small  amount  of  water  vapor. 
When  the  condensing  water  enters  the  lower  tubes  of  the  con- 
denser we  should  expect  that  curve  to  be  similar  to  B  at  the 
outset  and  similar  to  A  at  the  end,  while  with  water  introduced 
at  the  top  the  curve  should  start  out  with  the  greater  inclination 
and  end  with  the  lesser.  It  will  be  seen  from  Fig.  74  that  the 
curves  marked  "top"  and  "bottom"  have  this  difference  in 
character.     It  will  be  noticed  that  the  curves  for  the  greater 


CONDENSERS    AND    AIR   PUMPS  1 29 

rate  of  condensation  are  steeper  than  those  for  the  lesser  rate, 
and  in  some  places  steeper  than  curve  A .  This  shows  the  bene- 
ficial effect  of  velocity  of  steam  flow  over  the  tubes  as  this  pre- 
vents the  tubes  from  being  blanketed  by  the  air  which  tends  to 
collect  around  them.  At  the  greater  rate  of  condensation  the 
velocity  of  the  mixture  in  the  spaces  between  the  tubes  is  greater 
than  with  the  lower  rate  of  condensation. 

143.  Tube  Length.  —  The  curves  of  Fig.  74  may  be  used  also 
to  illustrate  the  effect  of  added  tube  length,  or  increase  of  sur- 
face for  a  given  amount  of  steam  to  be  condensed.  Any  surface 
added  to  a  condenser  is,  in  effect,  added  at  the  bottom  where  the 
air  predominates,  and  if  the  original  surface  was  sufficient  the 
added  surface  simply  increases  the  weight  and  cost  of  the  con- 
denser. If  a  condenser  has  a  rate  of  condensation  of  19.5  pounds 
per  square  foot  and  the  surface  is  increased  so  that  the  rate  is 
only  about  8.75  pounds  per  square  foot,  it  will  be  seen  from  Fig. 
74  that  about  one-third  of  the  surface  is  useless  since  there  is 
hardly  any  increase  in  the  temperature  of  the  water  passing 
through  the  bottom  tubes.  If  the  velocity  of  the  circulating 
water  had  been  decreased  in  the  latter  case  the  curve  would  not 
have  been  so  flat  in  the  region  of  the  bottom  tubes  and  the  size 
of  the  circulating  plant  could  have  been  decreased,  but  4.5  feet 
per  second  is  not  an  excessive  velocity  and  much  more  would  be 
gained  by  decreasing  the  cooling  surface. 

144.  Rate  of  Heat  Transmission.  —  Another  point  brought 
out  by  Fig.  74  is  the  low  rate  of  heat  transmission  for  air.  The 
water  passing  through  the  tubes  at  a  temperature  of  about  60°  F, 
extracted  but  little  heat  from  the  air  in  the  bottom  of  the  con- 
denser which  must  have  been  at  a  temperature  of  100°  or  more. 
There  is  lack  of  agreement  in  the  results  of  experiments  which 
have  been  made  upon  the  rate  of  heat  transmission  for  pure 
steam  but  roughly  speaking  we  may  expect  about  1000  B.t.u. 
per  hour  per  square  foot  of  cooling  surface  per  degree  dift'erence 
of  temperature  Fahrenheit,  when  the  cooling  water  has  a  velocity 
of  3  feet  per  second.  The  rate  of  heat  transmission  for  air  under 
the  conditions  which  exist  in  a  condenser  would  probably  not  be 
more  than  0.5  B.t.u.  per  hour  per  square  foot  of  cooKng  surface 


130      THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

per  degree  difference  of  temperature  Fahrenheit,  when  the  air 
has  a  velocity  of  20  feet  per  second  over  the  cooling  surface. 

145.  Velocity  of  Cooling  Water.  — •  The  effect  of  the  velocity 
of  the  cooHng  water  upon  the  rate  of  condensation  is  shown  by 
Fig.  75.     Curves  A  and  B  are  from  Mr.  Smith's  experiments,  A 


275 
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150 
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Vel.  Circ.  Water  Ft.  per  Sec. 

Fig.  75. 

for  practically  pure  saturated  steam  and  B  for  a  mixture  of  steam 
and  air  such  that  the  air  contributed  0.22  inch  mercury  to  the 
total  pressure,  the  temperature  being  110°  F.  The  initial  tem- 
perature of  the  cooling  water  was  70°  F.  and  the  surface  section 
ratio  was  553.  The  other  curves  were  obtained  from  Professor 
Weighton's  experiments  on  Contrafio  condensers.  The  fact 
that  the  curves  from  condenser  tests  are  practically  straight 
lines  shows  the  beneficial  effect  of  velocity  of  flow  of  gases  over 
the  cooling  surfaces.  In  curves  A  and  B  there  was  practically 
no  movement  of  the  gases  across  the  cooling  surface  and  as  the 
rate  of  condensation  increased  the  air  film  around  the  tubes 
thickened  and  the  rate  of  increase  of  heat  transference  was  not 
proportional  to  the  rate  of  increase  of  the  velocity  of  the  cooling 
water.  In  the  Contraflo  condenser  the  sweep  of  the  gases  over 
the  cooling  surface  prevented  to  a  large  extent  the  formation  of 


FIG.  76 


NOTE: 

Condenser  Shell  and  Tube   Sheets  to  have 
j  red  lead  joints. 

I  All  other  joints,  red   lead  and  canvas. 

4068  Tubes 

7986  Sq.  Ft.  of  Cooling  Surface. 

^22-5^' Rivets 

Wy,  1  2-'VJStuds 

p.c' 


Nary  Exhaust  (^VUin  Exhaust  Inlet 


Ford  V/ater  Chest 
I    \         ^___--rEye  Bolt 


Manhole  P 

33-%'RV>t3 
16-?4'Studs 

4->i"Studs 


J   tl. 


-Water  Chest  Cover 
(Upper) 


FORWARD 


Vi'ater  Chest  Cover 
(Lower) 


Handhole  Plate 


Fitted  with  1"  Tee  ;giving  a  drain  to  bilge 
and  a  steam  inlet  for  boiling  out. 

There  will  be  a  stop  valve  on  each 
connection. 


NOTE; 

Condenser  Shell  and  Tube  Sheets  to  have 
red  lead  joints. 
All  other  joints,  red  lead  and  canvas. 

4068  Tubes 
^_l_^  7986  Sq,  Ft,  of  Cooling  Surface. 

13|-P.C.~r9Vp.C." 
Nozzles  an'd  Scattering  Plates  shown  In  ! 

/vertical  position  for  convenience  in  drawing       ^^^  | 

iA„,l,i.,E.h=„., 


SECTION  ON  A-  B-C-D 


Vltted  with 


FIG.  77 


1"  Tee^giving  a  drain  to  bilge 
and  a  steam  inlet  for  boiling  out. 

There  will  be  a  stop  valve  on  each 
connection. 


CONDENSERS   AND   AIR   PUMPS 


131 


this  film  and  the  rate  of  condensation  increased  directly  as  the 
velocity  of  flow  of  the  cooling  water.  The  same  curves  show 
also  the  increase  of  rate  of  condensation  with  decrease  of  sur- 
face section  ratio.  This  increased  condensation  is  obtained, 
however,  at  the  expense  of  circulating  water,  more  water  per 
pound  of  steam  being  required  as  the  surface  section  ratio  be- 
comes smaller. 

CONDENSERS 

146.  Jet  Condensers.  —  There  are  two  types  of  condensers 
in  common  use,  the  Surface  and  the  Jet.  In  the  jet  condenser, 
see  Fig.  76,  the  steam  is  condensed  by  mixing  with  a  stream  of 
water  sprayed  into  the  condenser  in  a  finely  divided  form.  The 
condensing  water  and  the  condensed  steam  collect  at  the  bottom 
of  the  condenser  and  are  pumped  out  by  the  air  pump.  The 
condenser  must  be  large  enough  in  the  neighborhood  of  the  water 
spray  to  enable  the  steam  and  water  to  become  thoroughly 
mixed,  and  beyond  that  point  the  cross-sectional  area  can  be 
gradually  decreased  until  it  is  equal  to  the  area  of  the  air-pump 
suction  pipe.  There  is  no  way  of  figuring  the  size  of  the  conden- 
ser from  theoretical  considerations,  but  from  experience  we  find 
that  its  volume  should  be  about  one-third  of  the  volume  of  the 
L.P.  cyHnder.  This  type  of  condenser  costs  much  less  than  the 
Surface,  is  smaller  and  can  be  used  in  vessels  running  in  fresh 
water.  The  vacuum  obtained  is  usually  lower  than  that  given 
by  the  surface  condenser,  due  to  the  large  amounts  of  air  which 
come  in  with  the  condensing  water.  The  vacuum  usually 
obtained  is  around  22  inches  or  about  4  pounds  absolute. 

147.  Surface  Condensers.  —  The  surface  condenser,  see 
Fig.  77,  is  so  constructed  that  the  steam  is  condensed  by  coming 
in  contact  with  the  surface  of  tubes  through  which  cold  water  is 
circulated.  In  this  way  the  condensed  steam  and  condensing 
water  are  kept  separate  and  the  condenser  can  be  used  where  the 
condensing  water  is  not  of  a  character  suitable  for  feed  water. 
This  type  has  the  further  advantage  that  less  air  is  introduced 
into  the  system,  due  to  the  fact  that  the  same  feed  water  is  used 
over  and  over  again  and  the  amount  of  air  which  it  contains  is 
not  as  large  as  would  be  the  case  if  a  new  supply  were  constantly 


132      THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

introduced.  The  air  separates  from  the  water  in  the  boiler  and 
passes  through  the  engine  and  condenser  into  the  air  pump  where 
a  certain  amount  of  it  is  reabsorbed  by  the  water  during  com- 
pression. 

About  2  per  cent  of  make-up  feed  has  to  be  added  to  make  up 
for  losses  at  leaky  joints,  at  whistle,  and  in  blowing  off  scum. 
This  water  will  have  more  air  in  it  than  that  delivered  from  the 
air  pump.  However,  the  conditions  are  better  for  a  high  vacuum 
in  the  surface  condenser  than  in  the  jet  and  a  vacuum  of  26  inches 
is  easily  obtained.  The  surface  condenser  is  more  costly  in 
construction,  heavier,  occupies  more  space,  and  requires  more 
room  for  overhauling.  It  is  used  in  ^'essels  running  in  salt  water 
and  also  whenever  high  vacua  are  desired. 

The  amount  of  cooling  surface  needed  per  I.H.P.  varies  with 
the  vacuum  desired,  \^dth  the  construction  of  the  condenser,  and 
with  the  temperature  and  velocity  of  the  cooling  water.  In  the 
old  type  of  surface  condenser  where  a  vacuum  of  26  inches  is 
desired  it  is  found  that  i  to  1.25  square  feet  of  cooHng  surface 
per  I.H.P.  is  usually  sufficient  in  the  Temperate  Zone,  while  in 
the  Tropics  the  ratio  increases  to  1.75  square  feet  per  I.H.P. 

148.  Efficiency  of  Cooling  Surface.  —  More  attention  has 
been  given  to  condenser  design  lately  and  all  designers  agree 
that  it  is  essential  that  there  shall  be  no  dead  spaces  in  the  con- 
denser, but  that  the  steam  and  air  shall  have  as  nearly  as  possible 
a  uniform  speed  of  flow  over  the  entire  cooling  surface.  To  this 
end  the  cross-sectional  area  is  decreased  in  passing  from  the 
steam  inlet  to  the  air  pump  suction,  either  by  making  the  con- 
denser narrower  at  the  bottom,  or  by  means  of  diaphragms  so 
placed  that  the  area  for  passage  of  the  steam  and  air  continually 
decreases. 

The  efficiency  of  the  cooling  surface  increases  with  the  velocity 
of  the  gases  passing  over  it  but  since  the  increased  velocity  is 
obtained  only  by  an  increased  difference  in  pressure  between  the 
air  pump  suction  and  the  steam  inlet  this  increased  velocity 
means  a  greater  back  pressure  in  the  L.P.  cylinder  and  cannot 
be  carried  too  far. 

Another  principle  which  the  makers  of  the   Contraflo  con- 


CONDENSERS   AND   AIR   PUMPS  133 

denser  claim  is  of  great  importance  is  the  prevention  of  dripping. 
It  is  claimed  that  if  the  water  from  the  steam  condensed  by  the 
top  rows  of  tubes  is  allowed  to  drip  over  the  lower  rows  these 
tubes  serve  merely  to  cool  the  feed-water  and  do  not  condense 
steam  as  it  has  no  access  to  them.  To  obviate  this  diaphragms 
are  so  placed  in  the  condenser  that  the  water  of  condensation  is 


Weir-Uniflux  Condenser 

collected  and  carried  off  to  one  side  and  then  down  to  the  air 
pump  suction. 

The  condenser  cannot  be  considered  separate  from  the  air 
pump  as  the  efficiency  of  the  latter  reacts  upon  the  former.  If 
the  air  pump  is  not  of  sufficient  capacit}'  to  keep  the  condenser 
free  of  air  the  lower  tubes  will  be  drowned  in  air  and  the  steam 
will  have  no  access  to  them. 

The  rate  of  condensation  will  also  be  affected  by  the  velocity 
of  flow  of  the  cooling  water  through  the  tubes.     There  seems  to 


134      THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

be  no  reason  why  the  rate  of  condensation,  in  a  properly  designed 
condenser,  should  not  vary  directly  as  the  velocity  of  circulating 
water  through  the  tubes.  A  greater  velocity  of  flow  means  more 
work  for  the  circulating  pump  but  a  slight  increase  in  the  size 


Weir-Uniflux  Condenser 

and  power  of  this  pump  may  make  a  large  saving  in  weight  and 
cost  of  condenser. 

The  attention  paid  by  modern  designers  to  these  conditions 
which  make  for  a  more  efficient  cooling  surface  has  made  it 
possible  to  reduce  the  size  of  condensers  so  that  now  the  ratio 
of  cooling  surface  to  I.H.P.  varies  from  0.5  to  i,  depending  upon 
the  temperature  of  inlet  water  and  velocity  through  the  tubes. 


CONDENSERS   AND    AIR    PUMPS 


135 


149.  Comparison  of  Old  and  New  Types  of  Condensers.  — 
A  comparison  of  the  performances  of  the  old  and  new  type  of 
condenser  is  made  possible  through  the  extensive  experiments 
carried  out  by  Professor  Weighton  upon  a  Contraflo  condenser 
and  one  of  the  ordinary  type.  These  experiments  are  published 
in  the  Transactions  of  the  Institute  of  Naval  Architects,  Vol.  48, 

Relative  Performance  of  Condensers 
Inlet  Temperature  of  Water=50°  F. 
A-New  Type.  Cores  and  Spray,  "Dry"Air  Pump 
B-    "         "      Spray  only  "       "        " 

C-    "         "       Neither  Ordinary     "        " 

D-Old       "  "  "  "        "      -i|^=4.25 

E-Old       "  "  "  "        "      -if  =  10.7 

30 


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Lbs.  of  Condensing  Water  per  Lb.  of  Steam-^ 
Fig.  78. 

1906.  Curves  C,  D,  and  E  of  Fig.  78  show  the  relative  perform- 
ance of  two  condensers,  one  of  the  Contraflo  type  and  the  other 
of  the  old  type  found  in  many  ships,  with  the  condenser  a  part 
of  the  back  framing.  The  latter  condenser  had  f-inch  tubes  4 
feet  long,  with  a  cooling  surface  of  170  square  feet.  The  water 
made  two  passes  through  the  condenser,  giving  a  tube  length  of  8 
feet.  The  Contraflo  condenser  had  f-inch  tubes,  4  feet  long 
with  100  square  feet  of  cooKng  surface.     The  water  made  four 


136      THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

passes  through  the  condenser  gi\ing  an  effective  tube  length  of 
16  feet.  With  the  old  t^-pe  it  was  found  that  there  was  a  separate 
curve  for  each  rate  of  condensation,  the  surface  becoming  less 
efficient  as  the  rate  increased.  In  the  new  t>TDe  the  surface 
efficiency  was  practically  constant  and  one  curve  served  for  all 
rates  of  condensation. 

150.  High  Vacua.  —  With  the  introduction  of  the  steam 
turbine  the  necessity  arose  for  a  high  vacuum,  or  low  back  pres- 
sure, in  order  that  the  turbine's  highest  efficiency  might  be 
obtained.  With  the  reciprocating  engine  the  increase  in  effi- 
ciency is  considerable  as  the  back  pressure  decreases  up  to  a 
certain  point,  but  with  the  turbine  the  increase  is  much  greater. 
The  economy  in  steam  consumption  of  the  reciprocating  engine 
increases  about  1.5  per  cent  for  each  inch  increase  in  vacuum, 
while  with  the  turbine  an  increase  of  vacuum  from  26  to  27  inches 
gives  a  gain  of  about  4  per  cent,  from  27  to  28  inches  a  further 
gain  of  5  per  cent,  and  from  28  to  29  inches  a  further  gain  of  6 
or  7  per  cent  in  economy. 

The  condenser  for  the  reciprocating  engine  is  usually  designed 
to  give  a  vacuum  of  about  26  inches  and  the  discharge  from  the 
air  pump  will  be  115°  or  more  depending  upon  the  type  of  air 
pump  used.  While  the  efficiency  of  the  engine  alone  increases 
as  the  back  pressure  decreases,  the  decrease  in  temperature  of 
the  water  discharged  by  the  air  pump  may  counterbalance  this 
gain  when  we  consider  the  efficiency  of  engine  and  boiler  together. 
At  low  pressures  the  decrease  in  temperature  is  large  for  a  rel- 
atively small  decrease  in  pressure.  The  condenser  for  the 
turbine  is  designed  to  give  the  highest  practical  vacuum,  which 
is  about  28.5  inches  of  mercury  with  sea  water  of  60°  F.  In  the 
case  of  the  turbine  the  increase  in  economy  due  to  decreased 
back  pressure  is  sufficiently  great  to  more  than  overcome  the 
thermal  loss  due  to  decreased  temperature  of  the  air  pump  dis- 
charge. With  this  vacuum  and  the  large  area  for  the  passage  of 
exhaust  steam  from  turbine  to  condenser  the  steam  can  be 
expanded  down  to  about  i  pound  absolute. 

151.  Means  Employed  to  Obtain  High  Vacua.  —  The  means 
employed  to  obtain  low  condenser  pressures  may  be  considered 


CONDENSERS   AND   AIR    PUMPS  137 

under  four  heads:  (i)  the  wet  and  dry  air-pump  system,  (2) 
an  augmentor  condenser,  (3)  two-stage  air  pumps,  and  (4) 
rotary  air  pumps.  In  the  wet  and  dry  air-pump  system  a  wet 
pump  is  employed  to  remove  the  hot  water  and  a  so-called  "dry" 
air  pump  is  used  to  remove  the  air.  In  this  way  the  condensed 
steam  can  be  taken  off  at  as  high  a  temperature  as  possible  and 
used  for  feed- water,  while  the  "dry"  air  pump  is  supplied  with 
a  small  amount  of  cold  water  which  cools  the  air,  seals  the  valves, 
and  fills  the  clearance  spaces.  It  is  impossible  to  create  a  vacuum 
in  the  barrel  of  an  air  punip  in  the  presence  of  water  whose  tem- 
perature is  very  close  to  the  temperature  corresponding  to  the 
vacuum  desired.  The  evaporation  of  this  hot  w^ater  will  be  so 
rapid,  as  the  pressure  is  decreased  in  the  barrel,  that  the  vacuum 
will  be  spoiled.  Let  us  take  the  case  of  a  turbine  expanding 
down  to  I  pound  absolute.  The  average  pressure  in  the  condenser 
will  be  about  0.75  pound  absolute  and  the  air  pump  will  have  to 
develop  a  vacuum  of  about  0.5  pound  absolute  in  order  to  cause 
the  air  to  flow  into  the  pump.  The  temperatures  corresponding 
to  these  pressures  are  102°,  92°,  and  80°,  respectively.  The 
largest  part  of  the  steam  will  be  condensed  at  the  higher  tem- 
perature, about  100°,  and  unless  the  water  is  cooled  down  to 
about  75°  it  will  be  difficult  to  obtain  a  pressure  of  0.5  pound 
absolute  in  the  air  pump.  In  a  condenser  of  the  ordinary  type 
developing  a  vacuum  of  25  inches,  or  about  2.5  pounds  absolute, 
with  a  single  air  pump,  the  temperature  of  the  discharge  water 
will  be  about  115°,  although  the  temperature  corresponding  to  2 
pounds  absolute,  the  pressure  in  the  pump  barrel,  is  about  125°; 
showing  that  the  temperature  of  the  water  in  the  air-pump 
barrel  is  some  10°  less  than  that  corresponding  to  the 
vacuum. 

In  some  of  the  newer  types  of  condenser  this  separation  is 
effected  by  having  two  nozzles,  one  for  the  condensed  steam  and 
one  for  the  air.  The  lower  tubes  of  the  condenser  are  used  for 
cooling  the  water  supplied  to  the  dry  air  pump.  Fig.  78  shows 
the  effect  of  the  wet  and  dry  air-pump  system  upon  the  efficiency. 
Curve  B  is  for  the  condenser  wath  a  wet  pump  to  remove  the  hot 
water  and  a  spray  of  cold  water  introduced  into  the  air  suction 


138      THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


pipe  of  the  dry  air  pump.  Curve  C  is  for  the  same  condenser 
with  a  single  air  pump  to  remove  the  air  and  water  together. 
The  water  used  in  the  spray  is  inchided  in  the  pounds  of  water 
per  pound  of  steam. 

152.  Augmentor  Condenser.  —  Condensers  to  be  used  with 
Parsons  turbines  are  often  fitted  with  an  augmentor  as  shown 
in  Fig.  79.     At  A  there  is  an  ejector  wliich  picks  up  the  air  in  the 


CiRc.  Water  I^LET 
TO  Augmentor  Cond 


Augmentor  Nozzle 
Steam  to  Augmentor 


Fig.  79. 

condenser  at  low  pressure  and  delivers  it  to  the  air  pump  at  a 
higher  pressure,  the  difference  in  pressure  between  the  air  pump 
and  condenser  being  maintained  by  the  column  of  water  B  on  one 
side  and  by  the  momentum  of  the  mo\ing  stream  of  air  and  steam 
on  the  other.  In  this  way  an  air  pump  which  is  capable  of  main- 
taining a  vacuum  of  only  26  or  27  inches  in  the  air-pump  barrel, 
can  by  the  assistance  of  the  ejector  handle  a  sufficient  quantity 
of  air  to  maintain  a  vacuum  of  28  inches  or  28.5  inches  in  the 
condenser.  According  to  Mr.  Gerald  Stoney,  the  use  of  the 
augmentor  increases  the  economy  7  per  cent  while  the  steam 
used  is  only  7  to  8  per  cent  of  the  steam  saved. 

153.  Two-stage  Air  Pumps.  —  In  the  two-stage  air  pumps 
the  compression  from  the  low  vacuum  pressure  up  to  the  atmos- 
pheric pressure  is  performed  in  two  or  more  stages.     The  Weir 


CONDENSERS   AND   AIR   PUMPS 


139 


85 


70 


G5 


60 


.55 


"Dual"  Air  Pump  is  an  example  of  tliis.  These  pumps  and  the 
rotary  air  pump  will  be  considered  later  under  the  head  of  Air 
Pumps. 

154.  Neilson's  Formula  for  Condenser  Design.  —  The  amount 
of  cooling  surface  which  a  condenser  should  have  in  order  that 
it  may  produce  the  desired 
vacuum  should  be  determined 
by  the  steam  consumption  of 
the  engine,  the  back  pressure 
in  the  L.P.  cylinder,  the  tem- 
perature of  the  cooling  water 
at  inlet,  the  velocity  of  the 
cooHng  water  through  the  tubes, 
and  the  pounds  of  steam  that  §, 
can  be  condensed  per  square 
foot  of  cooling  surface  per  hour 
per  degree  difference  of  tem- 
perature of  cooling  water  and 
steam.  There  are  hardly  any  w^s.so 
published  tests  of  ordinary  con- 
densers in  which  all  these 
quantities  were  observed.  Mr. 
Neilson  read  a  paper  before 
the  Institute  of  Engineers  and 
Ship-builders  in  Scotland,  in 
February,  1910,  entitled  "The 
Design  of  Surface  Condensers,"  in  which  he  gave  the  following 
equation : 

W  =  Ske,n.  (72) 

W  =  weight  of  steam  condensed  per  hour. 
S  =  square  feet  cooHng  surface  in  tubes. 
A'  =  pounds  of  steam  condensed  per  hour  per  square  foot 

of  surface  per  degree  mean  difference  of  temperature 

of  steam  and  condensing  water. 


A     .50 


£2|.45 
1,40 


.35 


25 


20 


2         3         4 

Pressure  Absoiute 

Lbs.  per  Sq.  Inch 

Fig.  80. 


"m    —    Iv 


-c. 


tv  =  temperature  °  F.  corresponding  to  vacuum  desired. 


I40      THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

ti  =  temperature  °  F.  of  condensing  water  at  inlet. 
to  =  temperature  °  F.  of  condensing  water  at  outlet. 
C  =  2.5  for  ordinary  condensers. 

Mr.  Neilson  gives  a  formula  for  calculating  K  and  the  curves 
of  Fig.  80  have  been  drawn  by  means  of  this  formula.  In  the 
same  paper  the  quantity  of  cooling  water  necessary  per  hour  is 
given  as 

1000  W 


Q  = 


tn 


/,■ 


(73) 


The  values  of  to  to  be  used  in  these  equations  are  given  by  the 
curve  of  Fig.  81. 


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155.  Weighton's  Experiments.  —  A  very  complete  set  of 
experiments  upon  the  newer  t^pe  of  condenser  was  carried  out 
by  Professor  Weigh  ton  and  the  results  are  published  in  "The 
Transactions  of  the  Institute  of  Naval  Architects,"  Vol.  48,  1906. 
The  results  there  given  have  been  put  into  a  different  form  by 
the  author  and  are  shown  in  Fig.  82.  The  experiments  were 
made  with  condensing  water  whose  inlet  temperature  varied 
from  45°  to  70°.  Variation  was  also  made  in  the  surface-section 
ratio,  or  ratio  of  the  surface  of  the  tube  element  exposed  to  steam 
to  the  cross-sectional  area  of  the  water  passage  through  the  tube. 
Two  of  the  experiments  were  upon  condensers  whose  surface- 
section  ratios  were  1070  and  1700,  run  in  connection  with  a  single 


CONDENSERS  AND   AIR   PUMPS 


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142      THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILL\RIES 

air  pump  of  the  ordinary  type.  Two  other  experiments  were 
upon  the  same  condensers  with  triangular  wooden  cores  placed 
in  the  tubes  so  that  the  surface-section  ratios  were  1810  and  2900. 
In  these  experiments  the  condenser  was  run  in  connection  with 
a  wet  and  a  dry  air  pump,  and  a  spray  of  cold  water  was  intro- 
duced into  the  air-pump  suction. 

156.  A  Method  of  Design  Based  upon  Weighton's  Experi- 
ments. —  The  curves  of  T  as  drawn  in  Fig.  82  are  determined 
by  only  two  points  but  it  was  assumed  that  the  difference  in  air 
pumps  would  cause  only  a  bodily  displacement  of  one  curve 
from  another  and  would  not  cause  the  curves  to  differ  materially 
in  character,  so  that  the  points  for  one  could  be  used  as  a  guide 
in  fairing  in  the  other.     The  curves  were  derived  as  follows: 

Let  W  =  KSv''  (T  -  T,),  (74) 

,  „  „    1000    W  f  N 

and  Q^CyzTJ:  ^75) 

W\  =  pounds  of  steam  condensed  per  hour. 

W  =  equivalent  pounds  of  steam  at  8  pounds  absolute  and 

hot-well  temperature  of  100°  F. 

total  heat  at  release  minus  heat  of  hot- well  ttt- 
_ _ Wf 

1070 
K  =  factor  to  be  determined  from  experiments. 

S  =  coohng  surface  of  tubes  in  square  feet. 

V  =  velocity  of  condensing  water  through  tubes  in  feet  per 
second. 

X  =  exponent  of  v,  to  be  derived  from  experiment. 

T  =  factor  to  be  derived  from  experiment. 
Ti  =  temperature  °  F.  of  condensing  water  at  inlet. 

Q  =  quantity  of  condensing  water  per  hour  in  pounds. 

C  =  factor  to  be  derived  from  experiment. 

From  (74)  and  (75)  we  can  derive  the  following: 
^      W  I    _i ,^       Q   T  -Tj 

KC  =  ^^'-^—^^^-=^  =  ^-^-^-  (76) 

5  -0^  T  -TiW     1000        S  1}'  1000  ^'  ^ 


CONDENSERS   AND   AIR   PUMPS  143 

The  velocity  of  the  water  in  the  tubes  will  be 

'= 2 

62.15  X  3600  X  A 
62.15  =  mean  between  the  weight  of  a  cubic  foot  of  water  at 
50°  F.  and  110°  F. 
A  =  total  area  in  square  feet  of  all  the  tube  elements  for  the 
passage  of  water.  The  number  of  tube  elements  is 
equal  to  the  total  number  of  tubes  divided  by  the 
number  of  times  the  water  passes  through  the 
condenser. 

s 
s  =  surface  section  ratio  =  area  in  square  feet  of  the  cool- 
ing surface  of  one  tube  element  divided  by  the  area 
in  square  feet  of  the  water  passage  in  tube  element. 


V  = 


223,7405 


2^^^M4^..  (77) 

S  s 

"      W    S  s 

Formula  (78)  contains  some  of  the  quantities  usually  observed 
in  experiments  and  gives  the  relation  that  these  observed  quanti- 
ties should  bear  to  one  another.     ~  =  the  quantity  of  water  per 

W 

pound  of  steam,  and  —  =  the  pounds  of  steam  condensed  per 
o 

square  foot  of  cooling  surface. 

From  (76)  and  (77)  we  get 

j^^  ^  223,740  z"  L     I     =  yi-x  223.74 
.s         i'^  1000  s 

If  X  =    I , 

KC  =  ^i^.  (79) 

If  the  tubes  of  a  condenser  are  clean,  if  it  is  so  designed  that 
there  are  no  dead  spaces,  and  if  the  air  pump  is  of  sufficient 


144      THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

capacity  to  keep  the  lower  tubes  from  being  drowned  in  air,  the 
vahie  of  x  should  be  i ;  i.e.,  the  rate  of  condensation  should  vary- 
directly  as  the  velocity  of  the  condensing  water  in  the  tubes. 
It  is  not  impossible  for  x  to  be  greater  than  i  and  in  some  tests 
of  the  Contrafio  condensers  this  was  true.  The  more  rapid  the 
circulation  of  water  the  less  Hkelihood  is  there  of  a  solid  core  of 
water  going  through  the  tube  without  coming  in  contact  with 
the  sides. 

The  curves  of  Fig.  80  calculated  from  the  formula  given  by 
Mr.  Neilson  for  the  old  type  of  condenser  show  that  the  value 
of  X  is  about  0.42  for  a  29-inch  vacuum,  about  0.5  for  a  26-inch 
vacuum,  and  about  0.55  for  a  22-inch  vacuum.  This  formula 
contains  a  factor  which  makes  allowance  for  the  tubes  being 
dirty.  It  would  appear,  then,  that  under  the  most  favorable 
conditions  the  value  of  it;  =  i,  and  under  the  most  unfavorable 
=  0.5. 

Since  these  relations  exist  between  the  different  factors  the 
condensers  can  be  designed  by  means  of  the  curves  of  Fig.  82 
and  the  following  formulae: 


^      ^W''^iooo 

(75) 

Qs 

(77) 

223,740  y 

s 

(80) 

—  =  number  of  tube  elements. 
a 

(81) 

a  =  area  in  square  feet  of  the  water  passage 
in  one  tube  element. 

The  length  of  tubes  will  depend  upon  the  number  of  times  the 

water  is  to  pass  through  the  condenser. 

According  to  Formula  (79)  the  product  KC  is  constant  for 

22^  74 
V  =  I  and  is  equal  to  — ^-^— ^  irrespective  of  the  value  of  x.     It 

should  not  be  inferred  from  this  that  K  and  C  are  constant.     If 
the  tubes  are  dirty  so  that  ::c  <  i,  more  water  will  be  required  to 


CONDENSERS   AND   AIR   PUMPS  145 

condense  a  given  amount  of  steam  and  the  value  of  C  will  be 
larger  and  K  will  be  smaller.  Allowance  for  dirty  tubes  or  in- 
effective surface  can  be  made  by  increasing  the  values  of  C 
derived  from  experiments  on  condensers  with  clean  tubes. 

The  curves  of  Fig.  82  are  primarily  for  the  type  of  condenser 
experimented  on  and  do  not  necessarily  apply  to  any  other  type 
of  condenser. 

The  values  of  T  are  so  chosen  that  for  any  given  vacuum  the 
values  of  K,  or  C,  determined  from  the  results  of  the  test,  very 
nearly  coincide  for  the  different  values  of  T^.  For  instance,  take 
the  following  case: 

No.  2  condenser,  vacuum  =27  inches,  v  =  2. 

T  is  arbitrarily  chosen  to  be  114°. 


T 

W 
S 

w 

K 

^  . 

S{T  -  Ti) 

45 

^S-S 

0.225 

0.113 

55 

13-5 

0.  229 

0.115 

65 

II 

0.  224 

0. 112 

70 

10 

0.  227 

0. 114 

The  values  of  K  and  C  given  by  the  curves  of  Fig.  82  do  not 
in  the  worst  case  differ  more  than  2  per  cent  from  the  values  given 
by  Professor  Weighton,  and  in  most  cases  are  closer  than  2  per 
cent. 

The  values  of  K  decrease  as  the  surface-section  ratio  increases 
so  that  a  larger  amount  of  surface  must  be  used  for  the  larger 
surface-section  ratios.  The  quantity  of  water  necessary  to  con- 
dense I  pound  of  steam  will  decrease  as  the  surface-section  ratio 
increases.  Where  water  is  cheap  it  is  better  to  use  a  low  surface- 
section  ratio,  say  in  the  neighborhood  of  2000,  as  by  so  doing 
the  weight  of  the  condenser  can  be  cut  down  considerably  while 
the  extra  power  required  of  the  circulating  engine  will  not  in- 
crease its  weight  materially.  Where  water  is  expensive  a  higher 
surface-section  ratio  of  3000  should  be  used. 

157.  Velocity  of  Cooling  Water.  —  The  weight  of  the  con- 
denser can  be  reduced  by  running  the  water  through  the  tubes  at 
a  higher  velocity.     It  is  probable  in  the  old  types  of  condenser 


146      THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


this  velocity  has  been  as  low  as  i  foot  per  second  under  ordinary- 
conditions.  A  velocity  of  3  or  4  feet  per  second  can  be  used 
ordinarily  and  still  not  throw  an  undue  load  upon  the  circulating 
engine  if  the  velocity  has  to  be  increased  i  or  2  feet  per  second 
when  the  tubes  get  dirty  or  the  inlet  temperature  high. 

The  condensing  water  tends  to  pass  through  the  tubes  with  a 
central  core  more  or  less  unaffected  by  the  walls  of  the  tubes. 
As  the  quantity  of  condensing  water  is  increased  the  velocity  of 

Relation  Between  Outlet  Temp,  of  Condensing  Water,  Tq, 
AND  Temp.  Corresponding  to  Vacuum,  T^,. 
A-New  Type-Cores  and  Spray-"Dry"Air  Pump      Tj  =46° 
B-    "         "     -Spray  only  -     "        "        "  T^-  =46° 

C-   "         "     -Neither         -Ordinary     "        "  Tj-  =46° 

D-Old       "  "  "  "        "  Tt  =50° 


160 

IbO 

"^ 



r^ 

140 

' 

■^ 

^«« 

^ 

UU 

^ 

-^ 

120 

-.^ 

c^ 

^ 

\ 

t 

1  lU 

"^ 

"^ 

^^ 

^ 

S- 

\ 

s 

_l 

lOU 

\ 

'v     ^ 

Q. 

90 

D 

....^ 

B 

N 

Q. 

tiO 

"^ 

^\ 

\ 

\ 

V^ 

70 

■> 

A 

.^ 

T, 

60 

\ 

1 

\ 

50 
40 

\ 

22"         23"         24"         25"         26"         27" 

Vacuum  (30"  Barometer) 

Fig.  83. 


28" 


29" 


30" 


the  central  core  increases  faster  than  the  velocity  of  the  water 
in  contact  with  the  tube  walls.  This  will  cause  more  or  less 
eddying  and  cross-currents  due  to  pressure  differences  and  will 
bring  the  water  at  the  center  in  contact  with  the  tube  walls  to  a 
certain  extent.  The  greater  the  length  of  the  tubes  the  greater 
will  be  the  resistance  to  flow  along  the  tube  walls  and  the 
greater  will  be  the  eddying  and  cross-current  effect.  This  central 
core  of  unaffected  water  can  also  be  prevented  by  placing  a  tri- 


CONDENSERS   AND   AIR   PUMPS 


147 


angular  or  other  shaped  core  in  the  tube,  as  in  this  way  a  com- 
paratively thin  layer  of  water  passes  through.  Curve  A  of 
Fig.  83  shows  the  increase  in  efficiency  due  to  this  device.  These 
cores  increase  the  work  of  the  circulating  pump  and  care  must 
be  taken  that  the  velocity  chosen  is  not  so  high  that  this  increased 
work  neutrahzes  the  gain  from  the  increased  vacuum.  This 
device  could  be  used  where  condensing  water  was  scarce  and 
free  from  sediment  and  the  extra  power  demanded  of  the  circu- 
lating pump  would  cost  less  than  the  water  saved.  The  eflfect 
of  these  various  conditions  upon  the  outlet  temperature  of  the 
condensing  water  is  shown  by  Fig.  83. 

With  cores  in  the  tubes  and  the  dry  air  pump  cooled  by  the 
water  spray  the  final  temperature  was  the  same  as  that  due  to 


> 
a: 

i  30 
u 
S  29 

Relation  Between  Vacuum  and  Surface-Section  Ratio  at  G 
Values  OF-^.   Ordinary  Air  Pump.    T^- =50'^ 

iven 

Q_ 
w 

z:=z 

5:^ 

= 

= 

^___ 

= 

S   28 

UJ 

1 ^^      i   ^ 

40 

— 30 

25 

^^ 

^ 

^^ 

" 

- — 

X   27 
^   26 
5   25 

^^ 

'^ 

— ' 

20 

^ 

200  600         1000        1400        1800       2200        2600 

Surface  Section  Ratio 

Fig.  84. 


3000        3400       3800 


the  vacuum  at  the  condenser  top.  This  does  not  mean  that  the 
condensing  water  and  steam  are  at  the  same  temperature  for  it 
is  found  that  the  temperature  at  the  top  of  the  condenser  is 
always  in  excess  of  that  due  to  the  vacuum  registered.  The  low 
value  of  7^0  for  the  old  type  of  condenser  was  due  to  the  large 
diameter  of  the  tubes  relative  to  their  short  length. 

158.  Effect  of  Surface-section  Ratio.  —  In  the  experiments 
of  Professor  Weighton  it  was  found  that  the  surface-section  ratio 
affected  the  efficiency  in  the  manner  shown  by  the  curves  of 
Fig.  84.  The  maximum  efficiency  seems  to  be  obtained  with  a 
surface-section  ratio  of  about  3000.  According  to  these  curves 
a  vacuum  of  28  inches  could  be  obtained  with  20  pounds  of 


148     THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

water  per  pound  of  steam  and  a  surface-section  ratio  of  3000;  or 
with  25  pounds  of  water  per  pound  of  steam  at  a  surface-section 
ratio  of  1700;  or  with  30  pounds  of  water  per  pound  of  steam 
and  a  surface-section  ratio  of  1300,  etc. 

A  larger  surface-section  ratio  would  be  accompanied  by  a 
greater  weight  and  first  cost  of  condenser,  and  greater  first  cost 
of  circulating  engine,  but  by  increased  economy  in  condensing 
water.  If  water  is  cheap  it  would  be  better  to  use  a  smaller 
surface-section  ratio  than  that  giving  maximum  efficiency  in 
order  to  save  in  weight  and  first  cost  of  condenser  and  circu- 
lating engine. 

159.  Effect  of  Admitting  Water  at  Top  and  Bottom  of  Con- 
denser. —  It  is  common  practice  on  shipboard  to  admit  the 


2.^ 


^ 

.^. 

rrr' 

rrr 

^= 

— 

— 

— 

— 

— 

— I — 

r^ 

^' 

'6 

A-CONDENSING  WATER   ENTERS  AT  BOTTOM 

B-  "  "  <'        "  Top 

30 

29 

28 

27 

3  — 

o  o   25 
< 

>       25 

25    30    35    40    45    50    55    60    65    70    75    80    85     90 

Lbs.  of  Condensing  Water  per  Lb.  of  Steam^ 
Fig.  85. 

condensing  water  to  the  top  tubes  of  the  condenser  and  discharge 
it  from  the  bottom  tubes  in  order  that  the  water  from  the  con- 
densed steam  may  not  be  chilled  down  by  the  cold  entering  water. 
It  was  found  by  test,  however,  to  be  more  economical  to  have 
the  water  enter  the  lower  tubes  and  discharge  from  the  upper 
tubes.  Curves  A  and  B  of  Fig.  85  show  the  relative  effect  of 
the  two  methods  of  circulation.  The  steam  entered  the  top  of 
the  condenser  in  these  experiments. 

160.  Admission  of  Steam  to  Condenser.  —  Condensers  are 
sometimes  made  with  the  steam  entering  the  bottom  and  the 
air  is  taken  out  at  the  top.  The  steam  condensed  on  the  lower 
tubes  drips  down  and  meets  the  incoming  exhaust  and  is  heated 
by  it  so  that  the  temperature  of  the  discharge  to  the  feed  tank  is 


CONDENSERS   AND   AIR   PUMPS 


149 


quite  high.  This  method  makes  the  condenser  a  partial  jet 
condenser.  The  Alberger  Condenser  Company  make  a  con- 
denser of  this  type,  the  hot  water  being  taken  out  of  the  bottom 
of  an  elbow  in  the  exhaust  pipe. 

Condensers  have  been  made  with  the  steam  passing  through 
tubes  surrounded  by  water  but  this  method  puts  too  high  a 
back  pressure  on  the  engine,  as  the  resistance  to  the  flow  of 
steam  is  large,  and  it  is  not  easy  to  allow  for  the  constant  de- 
crease in  volume  occupied  by  the  steam  and  air.  This  causes 
the  velocity  to  be  large  at  entrance  and  small  at  exit,  whereas  a 
uniform  velocity  is  desirable. 

161.  Sizes  of  Condenser  Tubes.  —  Condenser  tubes  are 
usually  f  or  f  inch  in  diameter  and  the  thickness  is  18  to  20 
B.W.G.,  or  0.048  to  0.036  inch.  When  f-inch  tubes  are  spaced 
\^  inch  apart  the  number  of  tubes  per  square  foot  of  tube 
plate  is  about  135;  when  spaced  i  inch  apart,  about  125.  This 
includes  space  for  shell  clearance,  steam  passageways,  etc. 

A  paper  by  Mr.  William  Weir  in  the  "Transactions  of  the 
Institution  of  Engineers  and  Shipbuilders  in  Scotland,"  Oct.  22, 
191 2,  gives  the  following  information  concerning  condenser 
weights. 


Cargo  steamer  3000  H.P. 

Cargo  steamer  3000  H.P. 
Cargo  steamer  3000  H.P. 

Cross  channel 

Atlantic  liner 

Destroyer  (1900) 

Destroyer  (1912) 

Cruiser  (1907) 

Cruiser  (1912) 

Battleship  (1906) 

Battleship  (1912) 


Sea 

Vacuum, 

temper- 

inches 

ature. 

°F. 

23 

85 

23 

85 

25 

85 

28.5 

55 

28. 5 

60 

26s 

55 

28 

55 

27 

55 

28.3 

55 

28. S 

55 

28.5 

55 

Shell 
material 


CI. 

Steel 

Steel 

Steel 

Steel 

Brass 

Steel 

Gun  metal 

Steel 

Gun  metal 

Steel 


Type  of 
condenser 


In  engine  I 
frame     | 
Circular 
Uniflux 
Uniflux 
Uniflux 
Oval 
Uniflux 
Circular 
Uniflux 
Circular 
Uniflux 


Weight 

per 
I.H.P., 
pounds 


8.3 


Type  of 
engine 


Recip. 

Recip. 

Recip. 

Turbine 

Turbine 

Turbine 

Turbine 

Turbine 

Turbine 

Turbine 

Turbine 


AIR   PUMPS 

162.  Relation  of  Air  Pump  and  Condenser.  —  The  air  pump 
and  the  condenser  arc  so  intimately  related  to  one  another  that 
they  should  be  considered  as  a  unit  rather  than  as  two  separate 
auxiliaries.     This    is    illustrated    by    Mr.    Neilson's    statement: 


I50      THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

"The  function  of  the  condenser  is  to  reduce  the  ratio  of  steam  to 
air  by  the  condensation  of  the  greater  part  of  the  steam,  so  as  to 
diminish  the  volume  of  mixture  of  air  and  steam  which  has  to  be 
discharged  by  the  air  pump.  The  function  of  the  air  pump  is 
to  keep  down  the  ratio  of  air  to  steam  in  the  condenser,  so  as 
to  allow  the  cooling  surface  of  the  latter  to  act  effectively." 

163.  Neilson's  Diagram.  —  We  have  already  considered  the 
effect  of  air  in  the  condenser  upon  the  rate  of  condensation.  The 
effect  of-  vapor  in  the  mixture  delivered  to  the  air  pump  is  shown 
by  a  diagram  constructed  by  Mr.  Neilson,  see  Fig.  86.  It  will 
be  seen  that  for  any  given  vacuum  as  the  ratio  of  air  to  vapor 
decreases  the  volume  of  air  to  be  handled  by  the  air  pump  in- 
creases very  rapidly.  The  diagram  also  shows  the  marked  de- 
crease in  the  volume  to  be  handled  by  the  air  pump  caused  by 
lowering  the  temperature  for  a  given  vacuum.  This  again 
emphasizes  the  desirability  of  intercepting  the  condensed  water 
as  early  as  possible  and  removing  it  while  hot,  and  then  cooling 
the  air  and  vapor  by  some  means. 

164.  McBride's  Diagram. — ^The  same  diagram  can  be  used  for 
the  determination  of  the  amount  of  air  present  in  the  steam  when 
entering  the  condenser,  a  point  discussed  by  Mr.  McBride  in  a 
paper  before  the  American  Society  of  Mechanical  Engineers, 
June,  1908.  Mr.  McBride  assumes  that  one  part  of  air  to  10,000 
parts  of  steam  is  present  in  the  steam  as  it  enters  the  condenser. 
The  air  bears  such  a  small  ratio  to  the  steam  that  the  latter  will 
be  practically  saturated,  and  both  air  and  steam  can  be  con- 
sidered as  under  the  same  pressure  and  at  the  temperature  cor- 
responding to  that  pressure.  As  the  steam  and  air  pass  through 
the  condenser  the  steam  is  condensed,  the  temperature  falls,  and 
in  the  air-pump  suction  pipe  we  have  saturated  air  whose  volume 
will  depend  upon  the  temperature,  assuming  the  pressure  to  be 
unchanged  in  passing  through  the  condenser.  While  at  the 
entrance  to  the  condenser  the  air  would  have  a  volume  deter- 
mined by  the  absolute  pressure  at  that  point,  in  the  air-pump 
suction  the  air  will  have  a  volume  determined  by  its  partial 
pressure,  and  this  again  will  depend  upon  the  temperature  of  the 
mixture.     Mr.  McBride  expresses  this  volume  in  terms  of  the 


CONDENSERS  AND   AIR   PUMPS 


151 


o 


o 

> 


4200 


4000 


3800 


3600 


3400 


3200 


3000 


2800 


2600- 


<  2400 


50°  60°'  70°  80°  90°  100°  110°  120°  130°  140°  150° 
Temp-  -°Fahr. 
Fig.  86. 


152      THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

volume  of  i  pound  of  condensed  steam.  Thus,  if  the  vacuum  at 
entrance  to  the  condenser  is  28.5  inches  the  temperature  will  be 
92°  F.  and  the  absolute  pressure  0.7368  pound.  The  volume 
of  I  pound  of  steam  at  this  pressure  will  be  about  445  cubic  feet. 
If  I  volume  of  air  to  10,000  volumes  of  steam  is  present  the 
volume  of  air  at  entrance  will  be  0.0445  cubic  foot  in  every  pound 
of  steam.  If  the  pressure  in  the  air-pump  suction  pipe  is  28.5 
inches  and  the  temperature  is  80°  F.,  the  steam  will  exert  a 
pressure  of  0.505  pound.  The  pressure  of  the  air  will  then  be 
0.7368  —  0.505  =  0.2318  pound  per  square  inch.  The  volume 
of  the  air  will  be 

^^  0.7368  ^,  459.5  +  80  o        u-     r      . 

0.0445  X  —^ —  X  ^tJ^-^ =  0.138  cubic  foot. 

0.2318      459.5  +  92 

The  volume  of  i  pound  of  water  at  this  temperature  will  be 

=  0.01605.     0-138  -^  0.0165  =  8.36. 

62.25 

The  air  pump  would  need  a  capacity  of  9.36  X  volume  of  steam 
condensed. 

Mr.  Neilson's  diagram  can  be  calculated  from  a  formula  de- 
rived as  follows : 

_  12.387  X  /  X  14-7  _  0-3705  i  /o^N 

^-      49^.5{P-P)      ~  P-P'  ^^"^ 

12.387  =  volume  of  i  pound  of  air  at  32°  F. 

P  =  absolute  pressure  of  mixture  in  air-pump  suction. 
/  =  absolute  temperature,  F,  of  mixture  in  air-pump  suction. 
p  =  absolute  pressure  of  saturated  steam  at  temperature  t. 
Mr.   McB ride's  diagram  can  be  calculated  from  a  formula 
derived  as  follows: 

5=— ^X^Xt^^X-.  (83) 

10,000      T      [P  —  p)      w 

P,  t,  and  p  are  as  above. 
V  =  volume  of  i  pound  of  saturated  steam  at  pressure  P. 
T  =  absolute  temperature  of  saturated  steam  at  pressure  P. 
w  =  volume  of  i  pound  of  water  at  temperature  /  (cubic  feet) . 


CONDENSERS   AND   AIR   PUMPS  1 53 


At  50°  F.  -—  =  0.595,  -  =  62.4. 

1  w 

PV  I 

At  120°  F.  ";rr  =  0-592,  —=61.7. 

1  w 


Therefore  at  50°  F. 


and  at  120°  F. 


..  0.003715^ 
^"     P-P 


„  _  0.00366  t 


P-P 

A 

For  all  practical  purposes  B  = 

100 

165.  Determination  of  Air  Leakage.  —  We  can,  therefore, 
use  Fig.  86  for  the  determination  of  air  leakage  into  a  condenser 
by  simply  dividing  the  ordinates  by  100.  For  the  purpose  of 
illustration  take  a  case  where  the  following  quantities  are  known: 
28-inch  vacuum,  or  P  =  0.9823  pound  absolute;  /  =  95°  F. 
=  554.5°  absolute;  also  the  volume  of  water  pumped;  the  stroke, 
diameter,  and  number  of  double  strokes  of  the  air  pump.  Allow- 
ing for  slip,  the  volume  of  air  and  water  pumped  can  be  found  and 
divided  by  the  volume  of  water  pumped;  let  this  equal  40.  Then 
the  ratio  of  air  to  water  will  be  39  to  i.  From  Fig.  86  we  see 
that  for  the  vacuum  and  temperature  given  one  part  of  air  to 
10,000  parts  of  steam  would  give  a  ratio  of  12  to  i  in  the  air- 
pump  suction  pipe.  Therefore  in  this  case  the  proportion  of 
air  to  steam  at  entrance  to  the  condenser  is  3.25  in  10.000.  In 
this  way  one  can  determine  whether  the  air  leakage  into  a  con- 
denser is  normal  or  abnormal. 

166.  Air  Leakage  Allowed  for  by  Manufacturers.  —  Mr. 
McBride  states  that  manufacturers  of  vertical  twin  air  pumps 
for  surface  condensers  for  a  vacuum  of  26  inches,  and  a  tempera- 
ture of  110°  F.  in  the  hotwell,  furnish  a  pump  capable  of  dis- 
placing about  13  times  the  water  to  be  pumped.  From  Fig.  86 
we  see  that  this  allows  for  about  4  parts  of  air  to  10,000  of  steam. 
The  volume  would  be  made  up  about  as  follows: 


154      THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 

Condensed  steam i .  o  volume 

Air  in  feed-water  (i|  per  cent  by  volume) .       0.3  volume 
Air  leakage 11. 7  volumes 


13.0  volumes 

In  the  case  of  horizontal  air  pumps  for  a  26-inch  vacuum  and 
110°  F.  temperature  of  hotwell,  Mr.  McBride  states  that  allow- 
ance is  made  for  a  displacement  of  about  20  times  the  volume 
of  the  water  of  condensation. 

Where  jet  condensers  are  used  for  a  vacuum  of  26  inches,  hot- 
well  temperature  of  110°  F.,  injection  temperature  of  70°  F.,  and 
discharge  temperature  of  110°  F.,  the  displacement  of  the  pump 
is  made  52  times  the  volume  of  the  water  of  condensation.  The 
volumes  would  be  about  as  follows: 

Condensed  steam i .  o  volume 

Air  in  feed- water  (i^  per  cent  by  volume) . .       0.3  volume 

Condensing  water 26.0  volumes 

Air  in  condensing  water  (2  per  cent  by  volume)  1 1 .  o  volumes 
Air  entering  by  leakage 13.7  volumes 


52.0  volumes 


Mr.  McBride  assumes  from  these  allowances  by  manufacturers 
that  in  ordinary  land  practice  the  leakage  of  air  into  engines  is 
about  in  the  ratio  of  4.5  parts  per  10,000  parts  of  steam. 

167.  Air  Leakage  in  Delaware's  Engines.  — -  The  tests  of  the 
U.S.S.  Delaware  gave  data  from  which  the  following  air  leakages 
have  been  computed. 


21 .56  knots. 
19  knots. . . . 
12  knots. . . . 


Vacuum 

Hot- 
well 
temper- 
ature 

Pres- 
sure in 

2nd 
rec,  ab- 
solute 

I.H.P. 

Volumes  of 
air  per 
10,000 

volumes  of 
steam 

Double 
strokes  of 
air  pump 
per  minute 

26.3 
27.2 
28 

104.5 
89.7 
90.6 

37 

43-5 

14-5 

28,578 

16,602 

3.905 

2.65 
5-53 
8.7 

20.2 
21            < 
21.2 

Remarks 


M.P.  cut- 
off 
shortened 


CONDENSERS  AND   AIR   PUMPS  155 

Independent  air  pumps  are  usually  designed  to  give 
the  desired  displacement  at  20  to  30  double  strokes  per 
minute. 

168.  Air-pump  Capacity.  —  It  is  obvious  that  no  fixed  rule 
can  be  given  for  the  size  of  the  air  pump  as  it  will  depend  upon 
the  efficiency  of  the  condenser  in  removing  the  vapor  from  the 
air  and  upon  the  air  leakage  of  the  engine.  The  most  fruitful 
sources  of  air  are  the  L.P.  cylinder  and  valve  chest  and  the 
auxiliaries,  if  the  latter  exhaust  below  the  pressure  of  the  atmos- 
phere. The  air  coming  from  the  auxiliaries  can  be  eHminated 
by  putting  a  relief  valve  between  the  auxiliary  exhaust  line  and 
the  condenser  which  will  keep  the  exhaust  pressure  above  that 
of  the  atmosphere.  The  leakage  in  the  L.P.  cylinder  is  probably 
at  the  stuffing  boxes  of  the  piston  rod  and  valve  stems.  It  is 
noticed  that  when  the  engine  is  run  at  reduced  power,  with  the 
admission  pressure  to  the  L.P.  below  atmospheric  pressure,  it  is 
very  difficult  to  keep  a  good  vacuum.  This  leakage  at  the  piston 
rod  and  valve  stem  packings  can  be  eliminated  by  supplying 
the  stuffing  boxes  with  steam  from  the  intermediate  receiver  so 
that  there  will  be  a  tendency  for  steam  to  escape  from  the  boxes 
rather  than  for  air  to  leak  in. 

The  proportions  recommended  for  the  air  pump  vary  con- 
siderably as  the  following  will  show.  Mr.  LeBlanc  says  that  for 
turbines  with  a  29-inch  vacuum  the  air  pump  must  handle  21 
times  the  volume  of  water,  and  for  a  reciprocating  engine  with  a 
26-inch  vacuum  the  pump  must  handle  12  times  the  volume  of 
water. 

McBride  gives  the  following  as  stated  above: 

Vertical  twin  air  pump,  surface  condenser,  26-inch  vacuum, 
110°  F.  hotwell.  Pump  must  handle  13  times  the  volume  of 
water. 

Horizontal  air  pump,  same  condition  as  above.  Pump  must 
handle  20  times  volume  of  water. 

Jet  condensers,  same  condition  as  above  and  70°  F.  inlet 
temperature  of  injection.  Pump  must  handle  52  times  volume 
of  feed- water. 

Neilson  gives  the  following: 


156      THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


4-7t, 


Proportions  of  condenser  and  air  pump  should  be  such  that, 

cu.  f  t.  (work,  stroke)  air  pump  displacement  per  hour  _ 
sq.  ft.  condensing  surface 

or  4  to  7^  cubic  feet  air-pump  displacement  for  i  square  foot  of 
cooling  surface.  If  each  square  foot  of  cooHng  surface  condenses 
20  pounds  of  steam  this  would  result  in  allowing  an  air-pump 
displacement  of  12.5  to  23  times  the  volume  of  water. 

Professor  Weighton's  experiments  showed  that  a  vacuum  of  29 
inches  could  be  produced  if  there  was  a  displacement  of  0.7  cubic 
foot  for  every  pound  of  steam.  This  is  equivalent  to  a  displace- 
ment of  43.5  times  the  volume  of  water. 

A  28|-inch  vacuum  was  produced  with  0.3  cubic  foot  of  air- 
pump  displacement  per  pound  of  steam,  or  a  displacement  of 
18.6  times  the  volume  of  water  to  be  pumped. 


Authority 

Description 

Vacuum, 
inches 

Feed 
temper- 
ature 

Ratio  of  pump 

displacement 

to  water  pumped 

McBride. . .  . 
McBride.. .  . 
McBride 

Neilson.  ... 

Weighton. . . 
Weighton. . . 

Vert,  twin  pump,  surf.  cond. 
Hor.  air  pump,  surf.  cond. 
Jet  cond.  inlet  water  at  70° 
Surface  condenser,  20  pounds 

of  steam  per  square  foot  of 

cooling  surface 
Surface  condenser 

26 
26 
26 

26  to  28^ 

29 
28I 

no 
no 
no 

13 
20 

52 

12.5  to  23 

45 
20 

Surface  condenser 

169.  Attached  Air  Pumps.  —  In  marine  engine  practice  it  is 
customary  to  determine  the  size  of  an  attached  air  pump  (i.e., 
one  which  is  run  by  means  of  levers  from  one  of  the  crossheads) 
by  the  size  of  the  L.P.  cylinder. 

volume  of  L.P.  cylinder 
C 


Volume  of  air  pump  = 


(84) 


Triple  engine,  surface  condenser,  C  =  15  to  20. 

Triple  engine,  jet  condenser,  C  =  12.5. 

Compound  engine,  surface  condenser,  C  =  10. 
Compound  engine,  jet  condenser,         C  =  ^. 

The  attached  air  pump  will  always  be  larger  than  necessary 
for  full  power  if  it  is  made  large  enough  for  reduced  powers. 


CONDENSERS   AND   AIR  PUMPS 


157 


With  independent  pumps  it  is  found  that  the  number  of  double 
strokes  per  minute  will  remain  about  the  same  for  reduced  powers 
as  for  maximum  power.  The  greater  air  leakage  which  occurs 
at  reduced  powers  requires  a  greater  displacement  relative  to 
the  amount  of  water  used.  If  the  pump  is  attached  to  the  main 
engine  its  capacity  will  decrease  as  the  revolutions  decrease,  so 


Four-cylinder  Triple-expansion  Engine  with  Attached  Pumps  and  Weir-Uniflux 

Condenser. 

that  unless  it  is  made  larger  than  necessary  for  full  power  it  will 
not  be  sufficient  at  reduced  powers. 

170.  Air-pump  Proportions.  —  The  speed  of  the  bucket  should 
be  from  200  to  300  feet  per  minute,  the  lower  speed  to  be  used 
with  jet  condensers.  The  speed  of  the  water  and  air  through 
the  valves  will  be  greater  than  this,  as  the  net  area  through  the 
valves  is  usually  from  22  to  25  per  cent  of  the  area  of  the  bucket. 
The  Hft  of  the  valves  should  be  |  of  the  diameter.  The  con- 
struction of  the  valves  is  shown  in  Fig.  87  and  their  arrangement 
in  Fig.  88. 


158     THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILIARIES 


Fig.  87. 


CONDENSERS   AND   AIR   PUMPS 


159 


The  velocity  of  the  air  and  water  through  the  air-pump 
suction  pipe  should  be  from  10  to  15  feet  per  second  based  upon 
the  effective  strokes  of  the  pump.  The  size  of  the  discharge 
pipe  can  be  much  smaller  as  the  air  is  much  reduced  in  volume 
when  discharged  from  the  pump. 

The  thickness  of  metal  in  the  body  and  ends  of  the  pump 
should  be  (0.167  X  diameter  of  pump)  +  0.25  inch. 


171.  Types  of  Air  Pumps.  — •  Air  pumps  can  be  divided 
roughly  into  four  classes: 

1.  Reciprocating  pumps  with  three  sets  of  valves. 

2.  Reciprocating  pumps  with  one  set  of  valves. 

3.  Compound  pumps. 

4.  Rotary  pumps. 

Fig.  89  is  an  example  of  a  pump  of  class  (i),  with  a  set  of  head 
valves,  bucket  valves,  and  foot  valves.  Fig.  90  shows  a  set  of 
indicator  cards  taken  from  such  a  pump.     It  will  be  seen  that 


l6o      THE  DESIGN  OF  MARINE  ENGINES  AND  AUXILL\RIES 


Fig.  89. 


CONDENSERS   AND   AIR   PUMPS  l6l 

the  pump  works  in  two  stages.  On  the  under  side  of  the  bucket 
the  pressure  varies  from  the  vacuum  to  a  pressure  about  half- 
way between  that  and  the  discharge  pressure.  On  the  upper 
side  of  the  bucket  the  pressure  varies  from  something  less  than 
the  upper  pressure  of  the  under  side  to  the  discharge  pressure 
of  the  upper  side.  The  discharge  pressure  will  depend  upon 
whether  the  pump  is  discharging  into  a  hot  well,  as  with  a  sur- 
face condenser,  or  overboard,  as  with  a  jet  condenser.  The 
cards  shown  are  for  pumps  in  connection  with  jet  condensers. 


16-  SPRING 
BOT. 
2.25     e       

7 — "'=^::J^' 


TOP 

k     /^ 

"^-^4.5 

jy 

><frr'  g 

/-""i 

/ 

/ 

i^"       X  fh    ^'^'■'--..^ 


Fig.  90. 

The  lower  part  of  the  air  pump  is  in  communication  with  the 
condensers  from  about  a  to  b  (Fig.  90),  at  which  point  the 
bucket  is  at  the  top  of  its  stroke.  As  it  starts  down  the  foot 
valves  close  and  the  pressure  increases  from  b  to  c.  At  the  same 
time  the  pressure  on  the  top  of  the  bucket  drops  from  g  to  //. 
When  there  is  a  sufficient  pressure  difference  the  bucket  valves 
open  and  air  passes  through  the  valves  from  c  to  d.  At  that 
point  the  bucket  strikes  the  water  and  the  increased  resistance 
to  its  passage  through  valves  causes  the  pressure  to  rise  to  e. 
As  the  bucket  starts  upward  the  pressure  on  the  under  side  at 
first  drops  rapid  y  as  the  valve  closes  and  then  remains  nearly 
constant  up  to  /,  while  the  air  which  has  been  forced  into  the 
water  in  the  clearance  space  frees  itself.  The  events  on  the 
top  side  can  be  easily  followed  and  we  find  the  same  sudden 
increase  at  k  when  the  water  passes  out,  and  the  same  slowl}- 
falling  pressure  due  to  air  in  the  water  in  the  clearance  space. 
These  cards  show  very  plainly  that  even  with  water  in  the  clear- 
ance spaces  the  bad  effect  of  clearance  is  not  entirely  ob\iated. 


l62      THE   DESIGN   OF   MARINE   ENGINES   AND    AUXILIARIES 

The  Edwards  pump,  see  Fig.  91,  is  an  example  of  an  air  pump 
of  class  (2).     The  pressure  on  the  under  side  of  the  pump  is 

practically  constant  and 
equal  to  the  vacuum, 
while  on  the  top  the  pres- 
sure varies  from  that  of 
the  vacuum  to  something 
above  atmospheric  pres- 
sure. The  action  of  a 
pump  of  class  (i)  is  more  or 
less  intermittent.  There 
is  not  enough  difference 
in  pressure  between  the 
condenser  and  the  pump 
barrel  to  cause  the  water 
to  flow  through  the  foot 
valves  rapidly.  It  will 
accumulate  until  the  pres- 
sure due  to  its  own  head 
and  that  of  the  air  forces 
it  into  the  pump,  which 
for  a  few  strokes  will 
pump  only  water,  and 
then  only  air  while  more 


Fig.  91. 


water  accumulates.  In  the  Edwards  pump  the  flow  of  water 
does  not  depend  upon  the  pressure  difference  but  the  water  is 
caught  between  the  under  side  of  the  bucket  and  the  bottom 


Fig.  92. 

end  of  the  pump  and  forced  onto  the  top  of  the  bucket.  In  Fig. 
76  is  shown  a  double-acting  pump  of  class  (2).  Fig.  92  shows  a 
set  of  cards  taken  from  this  pump.     In  the  top  card  we  see  the 


CONDENSERS  AND   AIR   PUMPS 


163 


sudden  increase  in  pressure  when  the  water  passes  through  the 
top  valves.     On  the  under  side  of  the  pump  the  water  passes 


ll      II 


out  first,   then   the  air,  causing  the  pressure   to  run  up  to  a 
maximum  and  then  drop  as  the  air  passes  out. 

In  Fig.  90  it  will  be  seen  that  the  pump  is  open  to  the  condenser 
for  only  0.75  of  the  stroke,  due  to  the  slowness  of  the  bucket 
valves  in  closing  and  more  especially  to  the  escape  of  air  from 


1 64      THE   DESIGN  OF  MARINE   ENGINES   AND   AUXILIARIES 

the  water  in  the  clearance  space.  These  same  conditions  reduce 
the  time  that  the  bucket  valves  and  head  valves  are  open  to 
about  0.3  of  the  stroke.  These  diagrams  show  clearly  the  harm- 
ful effect  of  clearance  and  high  delivery  pressure. 

In  maintaining  a  vacuum  of  28  inches  or  more  with  pump  of 
class  I  or  2,  the  clearance  must  be  extremely  small  or  else  the 
operation  must  be  performed  in  a  greater  number  of  stages. 
This  increase  in  the  number  of  stages  can  be  effected  by  using 
two  Edwards  pumps,  one  delivering  to  the  other.  The  arrange- 
ment shown  by  Fig.  93  is  used  by  J.  G.  Weir  &  Co.,  where  a  high 
vacuum  is  desired.  It  can  be  readily  seen  that  the  water  will 
flow  to  pump  A  and  the  air  to  pump  B.  Pump  A  is  under  the 
steam  cylinder  as  this  is  the  pump  that  does  the  most  work. 
The  load  upon  B  is  slight  and  it  is  worked  by  beams  and  links 
from  the  piston  rod  oi  A.  A  portion  of  the  compression  of  the 
air  takes  place  in  the  lower  part  of  B,  and  it  is  stiU  further  com- 
pressed in  the  upper  part  of  5  to  a  pressure  of  about  5  pounds 
absolute.  It  is  then  delivered  to  the  upper  part  of  A  where  it 
is  brought  up  to  the  atmospheric  pressure  and  delivered.  The 
water  for  cooling  the  dry  pump  is  circulated  through  the  cooler 
as  shown,  the  circulation  being  maintained  by  the  difference 
in  pressure  between  the  suction  and  discharge  sides  of  the 
pump. 

Fig.  94  shows  a  LeBlanc  rotary  air  pump.  In  this  tj'pe  of 
pump  the  question  of  clearance  is  eliminated.  The  water  is 
thrown  towards  the  discharge  orifice  in  thin  sheets  and  carries 
the  air  out  in  this  way.  It  is  really  a  partial  admission  turbine 
running  backwards  and  delivering  energy  to  the  water.  Some 
tests  upon  this  pump  showed  that  it  required  about  one  I.H.P. 
for  2.2  pounds  of  water  per  second,  and  one  volume  of  water 
would  handle  four  volumes  of  air. 

172.  Condition  for  Maximum  Load.  —  In  estimating  the 
horse-power  of  an  air  pump  it  should  be  remembered  that  the 
maximum  horse-power  is  not  required  for  the  highest  vacuum 
but  for  a  back  pressure  of  about  8  or  9  pounds.     If  we  assume 

M.TL.P.  =  Pi'-±^  -  Pb, 
K 


CONDENSERS  AND   AIR   PUMPS 


165 


i 


l66      THE   DESIGN  OF  MARINE   ENGINES   AND  AUXILIARIES 


and  let 
then 


Fb 
M.E.P.  =  Fb  log, 


Fb 


If  we  differentiate  this  and  put  the  first  differential  =  o  we 

Fi 


find  that   the  M.E.P.  has  its  maximum  value  when 


Fb 


=  e 


=  2.7183,  and  when  this  relation  exists  the  M.E.P.  =  Fb.  As 
a  matter  of  fact  the  effect  of  clearance,  etc.,  is  such  that  the 
actual  M.E.P.  is  about  one-half  the  theoretical.  The  pump 
should  be  designed  mth  enough  power  to  produce  this  reduced 
vacuum,  if  conditions  are  such  that  the  higher  vacuum  cannot 
be  maintained. 

A  paper  by  Mr.  William  Weir  in  the  "Transactions  of  the 
Institution  of  Engineers  and  Shipbuilders  in  Scotland,"  Oct.  22, 
191 2,  gives  the  following  information  concerning  air  pumps. 


Steam 

Ratio  of  bucket 

Weight  of  pump 

Engine 

per 

Type  of  air 

Designed  vacuum, 

displacement  to 

per  H.P. 

I.H.P., 

pump 

inches 

volume  of  feed- 

of  main  engine. 

pounds 

water 

lbs. 

I 

17 

Twin 

26 

12.4 

2.0Q 

2 

IS 

Dual 

26 

7 

4 

I  .10 

3 

16 

Twin 

26 

IS 

4 

2.16 

4 

14 

Dual 

28.5 

13 

3 

1.38 

5 

14 

Dual 

28.5 

13 

2 

1.23 

6 

16 

Monotype 

26 

12 

7 

0.76s 

7 

14-5 

Dual 

28 

8 

8 

0.466 

8 

Attached 

25 

60 

9 

Attached 

25 

45 

10 

....j 

Attached 
Dual 

\  - 

26.5 

SECTION  V 
TURNING  ENGINES  AND  REVERSING  ENGINES 

TURNING    ENGINES 

173.  Type  of  Engine.  —  The  turning  engine  is  a  small  engine 
of  one  or  two  cylinders  used  for  turning  the  main  engine  over 
when  the  latter  is  being  overhauled  and  when  the  valves  are 
being  set.  The  engine  is  designed  to  turn  the  main  engine  over 
once  in  from  five  to  ten  minutes  and  since  the  r.p.m.  of  the 
engine  are  from  200  to  400,  the  turning  engine  makes  from  1000 
to  4000  revolutions  while  the  main  engine  is  turned  over  once. 
The  diameter  of  the  cylinder,  or  cylinders,  and  the  length  of  the 
stroke  are  usually  from  6  to  8  inches.  The  most  convenient 
means  of  making  this  large  reduction  in  revolutions  is  by  use  of 
worms  and  worm-wheels.  In  engines  of  1000  I.H.P.  or  less,  one 
worm  and  wheel  can  be  used  and  in  larger  engines  two  sets  are 
employed.  Small  engines  of  400  I.H.P.  or  less  are  usually 
turned  over  by  means  of  a  bar. 

If  the  worm  is  single  threaded  the  worm  wheel  will  advance 
one  tooth  for  each  revolution  of  the  worm,  and  with  the  arrange- 
ment shown  in  Plate  i  it  will  be  readily  seen  that  the  following 
relation  will  hold: 

rm  =  nn\.  (85) 

r  =  r.p.m.  of  turning  engine. 

m  =  number  of  minutes  to  turn  over  main  engine  once. 
n  =  number  of  teeth  on  smaU  worm-wheel. 
«i  =  number  of  teeth  on  large  worm-wheel. 

The  value  of  rm  is  usually  from  1000  to  2000  in  engines  under 
5000  I.H.P. 

174.  Frictional  Load.  —  The  frictional  load  which  the  turn- 
ing engine  has  to  overcome  is  hard  to  determine  exactly.     When 

167 


1 68      THE   DESIGN   OF   MARINE    ENGINES   AND    AUXILIARIES 

the  main  engine  is  not  under  steam  the  cylinder  walls  are  dry 
and  unlubricated  and  the  bearings  are  not  well  oiled.  The 
speed  at  which  the  main  engine  turns  is  so  very  slow  that  the 
coefficient  of  friction  will  be  practically  that  due  to  starting  a 
body  from  a  state  of  rest.  Experiments  have  shown  that  it 
takes  about  2.5  pounds  mean  effective  pressure  on  the  L.P. 
cylinder  to  overcome  engine  friction  when  running  at  a  piston 
speed  of  150  to  200  feet  per  minute.  If  we  assume  that  the 
coefficient  of  friction  from  a  state  of  rest  is  about  four  times  the 
coefficient  of  friction  at  200  feet  per  minute,  and  that  the  dry 
condition  of  bearings  and  cylinders  will  increase  the  frictional 
load  about  50  per  cent,  we  shall  have  the  frictional  load  to  be 
overcome  in  one  revolution  of  the  main  engine  as  follows: 

A  =  —X2S  X  M.E.P./  X  4  X  1.5.  (86) 

4 

D  =  diameter  of  L.P.  cylinder  of  main  engine  in  inches. 
5"  =  stroke  of  main  engine  in  inches. 
M.E.P./=  about  2.5. 

175.  Power  of  Turning  Engine.  — ■  The  power  of  the  turning 
engine,  driving  through  the  worm  and  wheels,  will  vary  accord- 
ing to  the  number  of  teeth  on  the  worm-wheels,  the  efficiency  of 
the  engine  and  gearing,  and  the  pressure  of  the  steam.  The 
engine  is  usually  run  from  the  auxiliary  steam  line  where  the 
pressure  will  be  100  pounds,  gage,  or  less.  The  power  finally 
delivered  to  the  main  engine  shaft  will  be  as  follows: 

B  ='^X  2sX  m.e.p.  X  n  X  iii  X  e  X  Ci  X  e^.  (87) 

4 

d  =  diameter  of  cylinder  of  turning  engine  in  inches. 
5  =  stroke  of  turning  engine  in  inches, 
m.e.p.  =  mean  effective  pressure  in  cylinder  =  about  0.75  P. 

P  =  steam  pressure  at  engine. 
n  and  n\  are  as  above. 

e  =  mechanical  efficiency  of  engine  =  about  0.8. 
d  =  efficiency  of  small  worm  and  wheel  =  about  0.4. 
e-2  =  efficiency  of  large  worm  and  wheel  =  about  0.4. 


TURNING  ENGINES   AND   REVERSING   ENGINES  169 

Equating  A  and  B  and  substituting  the  values  for  efficiency, 
etc.,  the  following  equation  is  obtained: 

^,^^g^XM.E.P.,x5X6,. 
nXniXF 

If  special  attention  is  paid  to  the  design  of  the  worm  and 
wheel,  and  if  the  worm  runs  in  a  bath  of  oil  and  has  a  thrust 
bearing,  the  efficiency  will  be  higher  than  0.4,  but  as  ordinarily 
designed  for  turning  engines  the  gears  will  have  about  that 
efficiency. 

176.  Proportions  of  Teeth  of  Worm  and  Wheel.  —  The  teeth 
of  the  worm  and  wheel  must  be  figured  to  stand  the  stress  re- 
sulting from  the  transmission  of  power,  and  in  order  that  they 
may  have  a  practical  thickness  at  the  root  it  is  usual  to  employ 
a  pitch  of  1.75  to  2.25  inches  on  the  small  worm-wheel,  and  of 
2.25  to  3.5  inches  on  the  large  worm-wheel.  The  proportions  of 
the  teeth  should  be  about  as  follows: 

Length  of  teeth  =  0.65  pitch. 

Face  of  teeth      =  0.3  pitch. 

Flank  of  teeth    =  0.35  pitch. 

Thickness  of  teeth  at  pitch  circle  =  0.48  pitch. 

Breadth  of  teeth  at  root  of  worm  wheel  =  2  to  2.25  pitch. 

Least  number  of  teeth  on  small  worm-wheel  about  25. 

177.  Design  of  Worm  and  Wheel.  —  Diameter  of  pitch  circle 
of  large  worm-wheel  =  CS 

C  =  I.I  to  1.5. 
Let  Z  =  inch-pounds  of  work  done  by  turning  engine  in  one 

stroke  =  0.75  P  — 5.  (89) 

4 

The  force  acting  upon  the  teeth  of  the  small  worm-wheel  at 
the  pitch  circle  will  be 

F  =  0.75  P  —  2  s  X  (0.8)  X  -  X  (0.6)  =  ^:96Z^  ^^^^ 

4  P  P 

p  =  pitch  of  teeth  on  small  worm-wheel  in  inches. 


lyo      THE   DESIGN    OF   MARINE   ENGINES   AND   AUXILIARIES 

It  will  be  noticed  in  the  above  equation  that  the  force  acting 
upon  the  teeth  is  taken  as  0.6  of  the  power  delivered  by  the 
engine,  although  the  efficiency  of  the  gear  is  taken  as  0.4.  It  is 
assumed  that  there  are  three  sources  of  frictional  loss,  the  end 
thrust  of  the  worm,  the  friction  in  the  bearing  of  the  worm-wheel, 
and  the  friction  between  the  teeth.  It  is  assumed  that  each  loss 
amounts  to  0.2  of  the  total  power  delivered  to  the  worm.  Upon 
this  assumption  the  power  delivered  to  the  teeth  will  be  0.6  of 
the  power  delivered  to  the  worm. 

The  force  acting  upon  the  teeth  of  the  large  worm-wheel  at  the 
pitch  circle  will  be 

„       2  „  ^^  pn  ^^  ,    ,s       0.384  Zn  (    . 

Fi  =  ~F  X^—X  (0.6)  =  -^-^ (91) 

Z  Pi  P^ 

pi  =  pitch  of  teeth  on  large  worm-wheel. 

Assume  that  the  force  acting  at  the  pitch  circle  is  carried  by 
two  teeth,  that  the  teeth  have  the  proportions  given  above,  and 
that  if  the  thickness  of  the  teeth  at  the  pitch  circle  is  0.48  p  the 
thickness  at  the  root  will  be  at  least  0.5  /?.  The  stress  at  the 
root  of  the  teeth  of  the  small  worm-wheel  will  be 

J.      F16      4.2F  ,    . 

^  =  76?=  ci/'  ^^'^ 

h  =  Cip  =  breadth  of  teeth  at  root. 
Ci  varies  from  2  to  2.5. 

/  =  length  of  teeth  below  pitch  circle  =  0.35  p. 
t  =  0.5  p. 

The  stress  at  the  root  of  the  teeth  of  the  large  worm-wheel 
will  be 

FJi  6      2.91  Fi  ., 

2  bih^        Copi 
h  and  hi  are  the  same  as  I  and  h. 

h  =  0.6  pi  when  thickness  of  tooth  at  pitch  circle  =  0.48  pi. 
Co  varies  from  2  to  2.50. 

The  stresses  allowed  are  3500  to  4000  pounds  for  cast  iron, 
and  5000  pounds  for  cast  steel.  It  is  advisable  to  make  the 
worm  of  steel  and  the  worm-wheel  of  cast  iron.     If  the  worm- 


TURNING   ENGINES   AND   REVERSING   ENGINES  171 

wheel  is  made  of  cast  steel  the  worm  should  be  made  of  bronze. 
If  the  teeth  of  the  worm  and  wheel  are  of  equal  thickness  at  the 
pitch  circle  the  teeth  of  the  worm  do  not  need  to  be  figured  as 
they  will  be  thicker  at  the  root  than  the  teeth  of  the  wheel. 

The  efficiency  of  worm  gearing  improves  as  the  pitch  angle  of 
the  worm  becomes  larger,  and  in  order  that  the  angle  may  be 
as  large  as  possible  for  a  given  pitch  the  diameter  of  the  worm 
should  be  as  small  as  possible.  The  worms  are  usually  made 
separate  and  are  keyed  to  the  shaft,  in  which  case  the  diameter 
of  the  pitch  cylinder  will  be  about  3  X  pitch.  This  diameter 
allows  for  a  thickness  of  metal  below  the  root  circle  of  about 
0.5  X  pitch.  If  the  worm  is  cut  from  the  shaft  forging  the 
diameter  of  the  pitch  cyHnder  can  be  about  2.5  X  pitch  of  the 
teeth.     The  length  of  the  worm  should  be  from  3  to  4  X  pitch. 

The  indicated  horse-power  of  the  turning  engine  will  be 

i.h.p.=   — (94) 

198,000 

The  mean  turning  moment  on  the  crank  shaft  will  be 

M  =  -■ 

IT 

The  maximum  turning  moment  \vill  be  about  2  M. 

The  bending  moment  on  the  crank  shaft  will  be  about  0.5  the 
maximum  twisting  moment.  The  diameter  of  the  crank  shaft 
can  be  determined  by  means  of  the  formula: 

diameter  of  shaft  =  Cs  X  i.72y/  — •  (95) 

M  =  maximum  twisting  moment. 

/  =  allowable  stress. 
Cs  has  values  depending  upon  the  ratio  of  bending  moment 
to  twisting  moment. 

bending  moment 

— : — 7-^ =  0.2 s-o .  "^o-o .  7 s-i . o-i .  2  =^-1 .  i;-!  .  7 K,-2. 

twistmg  moment  ^       J         /  j  o       o       /  o 

Cs  =  I. 09-1. I 7-1. 26-1. 34-1. 42-1. 49-1. 56-1. 62. 


172       THE   DESIGN   OF   MARINE   ENGINES   AND   AUXILIARIES 

The  mean  twisting  moment  upon  the  shaft  of  the  large  worm 
will  be 

M,  =^=i.53Zw.  (96) 

2  IT 

The  maximum  twisting  moment  will  be  about  1.25^^1  as  the 

flywheel  on  the  crank  shaft  will  cause  the  turning  moment  of  the 

small  worm  to  be  more  uniform.     The  small  worm-wheel  usually 

overhangs  the  bearing,  so  there  will  be  a  bending  moment  upon 

the  shaft  of  the  large  worm.     The  ratio  of  bending  moment  to 

^    .  ^.  ^     Ml  1     half  breadth  of  small  wheel 

twistmg  moment  will  be ;: — z — 

radius  of  small  wheel. 

Formula  (95)  given  above  will  serve  for  finding  the  diameter 
of  this  shaft  also. 

The  mean  twisting  moment  upon  the  main  engine  shaft  will 
be 

M2  =  -Fi-^  =  0.041  Znni.  (97) 

3       2  r 

The  relation  between  the  number  of  teeth  and  the  other  pro- 
portion of  the  large  worm-wheel  will  be  as  follows: 


or 


/l  = 

2.91  Ft 

Fi  = 

0.384  Zn 
Pi 

fi  = 

Znn\^ 

27.8C2C353' 

27.8/1C2C353 

ntii   — 

Z 

mil  = 

rm. 

m^  — 

27.SfiC2C'S^ 

"1 

Zrm 

n  = 

rm 

fii 

ni 


(98) 


(99) 

(100) 


n  should  not  be  less  than  25. 

The  large  worm-wheel  is  usually  made  in  halves  so  the  number 


TURNING   ENGINES   AND   REVERSING   ENGINES  173 

of  teeth  on  the  wheel  must  be  even.  The  quantities  should  be 
determined  in  the  following  order: 

Assume  r,  m,  M.E.P./,  and  F. 

Find  d,  s,  and  Z.     Use  Formulae  (88)  and  (89). 

Assume /i,  Co,  and  C  (these  values  may  be  changed  later). 

Find  Wi  and  n.     Use  Formulae  (99)  and  (100). 

Find  pi  (from  Wi  and  C)  and  Fi  [from  Formula  (91)]. 

Find  values  of  C,  C2,  and/i  (assumed  before)  which  agree  with 
results  already  found. 

Find  diameter  of  pitch  circle  of  large  worm-wheel  from  pi 
and  Wi. 

Solve  Formula  (93)  for  fi  with  the  finally  determined  values 
of  C  and  C2. 

Assume  p,  and  value  of  Ci  for  small  worm-wheel. 

Find  F  [from  Formula  (90)]  and/  [f  om  Formula  (92)]. 

Find  diameter  of  small  worm  wheel  from  p  and  n. 

Find  i.h.p.,  diameter  of  shafts,  diameters  and  lengths  of 
worms. 

It  will  be  noticed  that  certain  coefficients  and  quantities  have 
to  be  first  assumed  and  then  determined  exactly.  The  assump- 
tions do  not  always  give  practical  results  and  slight  changes  have 
to  be  made  to  get  whole  or  even  numbers  of  teeth,  and  to  get 
the  breadths  to  quarters  of  an  inch. 

REVERSING   ENGINES 

178.  Types  of  Reversing  Engines.  —  Reversal  of  motion  in 
marine  engines  fitted  with  Stephenson's  valve  gears  is  obtained 
by  throwing  the  links  over,  in  order  that  the  valve  stems  may  be 
actuated  by  eccentrics  properly  set  to  give  the  reverse  motion. 
In  engines  of  500  I.H.P.  or  less,  the  size  of  the  parts  is  such  that 
this  reversal  can  be  accomplished  by  hand,  but  in  large  engines 
the  friction  of  the  valves  and  stuffing  boxes  is  such  that  it  re- 
quires a  steam  engine  to  throw  the  links  over  quickly.  There 
are  two  types  of  reversing  engines  in  general  use  for  this  purpose, 
the  direct- acting  (see  Plates  i,  2,  and  3)  and  the  all-round  (see 
Fig.  95).  In  the  first  type  the  engine  is  directly  connected  to  the 
reverse  shaft  and  makes  only  one  stroke  in  reversing.     This 


174      THE   DESIGN  OF   MARINE   ENGINES   AND   AUXILIARIES 


necessitates  a  steam  cylinder  whose  diameter  is  from  0.19  to  0.2 
the  diameter,  of  the  L.P.  cylinder.  In  the  all-round  type  the 
power  is  obtained  from  one  or  two  small  cylinders  from  6  to  8 

inches  in  diameter  and  making 
from  200  to  400  r.p.m. 

One  advantage  of  the  all- 
round  type  is  that  there  is  less' 
danger  of  damage  from  careless 
handling,  and  another  advantage 
is  that  the  same  engine  can  be 
used  as  a  turning  engine  by  a 
proper  arrangement  of  gears  and 
couplings. 

179.  Direct-acting  Engine. — 
The  cyUnder  of  the  direct-acting 
gear  is  supplied  with  steam  at 
boiler  pressure  and  the  load  upon 
the  piston  rod  and  connecting 
rod  can  be  taken  as 

IV  =  BP  X  0.038  L.P.  area. 

(lOl) 

BP  =  boiler  pressure,  gage. 

The  diameter  of  these  rods  at 
the  middle  can  be  found  by 
means  of  Formula  (12),  or  by 
Fig.  22.  The  diameter  of  the 
connecting  rod  at  the  ends  can 
be  0.85  of  the  diameter  at  the 
middle.  The  length  of  the  piston 
rod  will  be  about  1.5  the  stroke  of  the  reversing  engine,  and  the 
stroke  of  the  reversing  engine  will  be  about  0.75  of  the  distance 
between  the  eccentric  rod  pins  on  the  Knks.  The  length  of  the 
connecting  rod  will  be  from  2  to  2.5  the  stroke  of  the  reversing 
engine,  depending  upon  the  relative  location  of  engine  and 
reverse  shaft. 

The  pin  connecting  the  piston  rod  and  connecting  rod  can  be 


Fig.  95. 


TURNING   ENGINES   AND    REVERSING   ENGINES  175 

designed  to  carry  a  bearing  pressure  of  3000  pounds  to  the  square 
inch,  since  the  swing  of  the  connecting  rod  is  very  small  and  the 
engine  is  not  in  use  a  sufficient  length  of  time  to  heat  the  pin. 
The  crosshead  guide  is  a  rod  of  circular  section  and  the  slipper 
encloses  it.  The  bearing  pressure  upon  the  sHpper  should  be 
from  60  to  80  pounds  per  square  inch.  The  maximum  load 
coming  upon  the  slipper  will  be 


2  •/  4 

r  =  length  of  reversing  engine  lever. 
^  =  stroke  of  reversing  engine  in  inches. 
/  =  length  of  reversing-engine  connecting  rod  in  inches. 
BP  =  boiler  pressure,  gage. 
d  =  diameter  of  reversing  engine  in  inches. 

The  length  of  the  crosshead  guide  will  be  about  equal  to  the 
length  of  the  piston  rod  and  the  diameter  of  the  rod  can  be  de- 
termined by  considering  the  guide  as  a  beam  of  circular  section 
supported  at  the  ends  and  loaded  at  the  middle  with  the  load  g. 

180.  All-round  Gear.  —  When  the  all-round  gear  is  used  the 
maximum  pull  in  the  drag  rod  (see  Fig.  95)  can  be  taken  as  w. 
The  pull  that  must  be  resisted  at  the  pitch  circle  of  the  worm 
wheel  will  be 

A  =  w- 
0 

=  5^X0.038^'^.  (103) 

a  =  radius  of  pin  (Fig.  95). 
h  =  radius  of  pitch  circle  of  teeth. 
D  =  diameter  of  L.P.  cylinder  of  main  engine. 

If  the  reversing  engine  has  a  mechanical  efficiency  of  0.8,  and 
if  the  efiiciency  of  the  worm  gearing  is  0.4,  we  shall  have  the 
power  deUvered  to  the  worm  wheel  at  the  pitch  circle  as  follows: 

^  =  /^  X  5P  X  ^^  X  2  ^  X  0.8  X  0.4  X  -•  (104) 

4  P 


176      THE   DESIGN   OF   MARINE   ENGINES   AND   AUXILIARIES 

F  =  ratio  between  the  m.e.p.  and  the  boiler  pressure  for 

the  reversing  engine. 
d  =  diameter  of  reversing  engine  cylinder  in  inches, 
.y  =  stroke  of  reversing  engine  in  inches. 
p  =  pitch  of  teeth  on  worm-wheel  in  inches. 

Equate  A  and  B  and  we  derive  the  following  formula: 

„        0.6  pD-a  ,       . 

d^s  =  -^^  (105) 

The  diameter  and  stroke  are  usually  between  6  and  8  inches. 
The  other  parts  of  the  gear,  such  as  crank  shaft,  worm,  and  worm- 
wheel,  can  be  designed  in  accordance  with  rules  given  under 
Turning  Engines. 

181.  Cushioning  Devices.  —  With  the  direct-acting  gear 
there  is  danger  that  the  cylinder  heads  may  be  carried  away  if 
the  piston  gets  too  great  momentum.  There  are  two  ways  of 
preventing  this:  (i)  by  means  of  an  oil  cylinder;  (2)  by  means 
of  exhaust  ports  placed  far  enough  from  the  ends  so  that  the 
piston  over-travels  them  and  a  certain  amount  of  steam  is 
caught  and  compressed.  In  the  case  of  the  oil  cyhnder  the  flow 
of  oil  from  one  side  of  the  piston  to  the  other  is  controlled  by  a 
valve  on  the  same  valve  spindle  as  the  steam  valve.  The  same 
motions  that  open  and  close  the  steam  valve  open  and  close  the 
oil  valve,  and  when  the  oil  valve  is  closed  the  gear  is  locked  in 
position.  By  throttling  the  oil  in  the  passage  from  one  side  of 
the  cylinder  to  the  other  the  rate  of  movement  of  the  piston  can 
be  controlled. 

The  valve  which  operates  the  steam  cylinder  may  be  a  flat 
slide  valve  or  a  piston  slide  valve.  If  the  latter  is  used  the 
steam  may  be  admitted  either  at  the  ends  or  at  the  middle. 
These  valves  overlap  the  edges  of  the  ports  by  not  more  than  -^q 
inch  on  the  steam  side.  Some  valves  are  made  "Hne  and  line," 
or  with  no  lap  at  all;  others  are  made  mth  a  clearance  on  the 
steam  side  so  that  in  the  ''ahead"  position  the  steam  pressure 
will  prevent  the  links  from  working  over  towards  mid-position. 
In  some  cases  the  piston  is  cushioned  by  means  of  an  exhaust 
lap  on  the  valve.     The  lap  of  the  oil  valve  should  be  only  enough 


TURNING  ENGINES   AND   REVERSING  ENGINES 


177 


Fig.  96. 


178      THE   DESIGN  OF  MARINE   ENGINES   AND   AUXILIARIES 


for  oil  tightness,  as  the  gear  will  be  locked  as  soon  as  this  valve 
is  closed. 


182. 

Plates 


Floating-lever  Gear.  —  In  the  type  of  gear  shown  in 
I,  2,  and  3,  the  valve  is  operated  by  means  of  a  floating 
lever  (see  ac,  Fig.  96).  This  lever  has 
three  points  of  attachment,  one  at  h 
for  the  valve  steam,  one  at  c  for  the 
reverse  lever  linkage  from  the  work- 
ing platform,  and  one  at  a  for  the 
reverse  gear.  The  valve  gear  is  so 
set  up  that  when  the  valve  is  moved 
in  one  direction  by  the  reverse  lever 
linkage  the  resulting  movement  of 
the  reverse  gear  brings  the  valve  back 
to  its  original  position.  The  valve 
does  not  open  the  full  width  of  the 
port,  but  stops  are  usually  arranged 
so  that  the  valve  cannot  open  more 
than  \  inch  or  so.  In  starting  to  use 
the  reverse  gear,  a  is  a  fixed  point  and 
a  movement  of  c  opens  the  valve. 
If  it  is  desired  to  keep  the  valve 
open,  h  must  become  a  fixed  point 
and  c  must  be  moved  by  the  hand 
lever  to  counteract  the  movement  of 
point  a  by  the  reverse  gear.  If  the 
reverse  gear  is  to  be  stopped  the 
reverse  lever  is  held  stationary  which 
makes  c  a  fixed  point  and  a  very 
slight  movement  of  a  closes  the  valve  and  the  gear  is 
stopped. 

183.  Brown  Gear.  —  In  the  Brown  gear  shown  in  Fig.  97  the 
floating  lever  is  replaced  by  a  valve  stem  with  a  fine  thread  on 
one  end  and  a  coarse  thread  on  the  other.  When  the  gear  is  to 
be  started  the  valve  is  opened  by  raising  or  lowering  the  nut  d. 
The  nut  e  is  attached  to  the  crosshead  and  the  movement  of  the 
nut  along  the  thread  causes  the  spindle  to  turn.     If  the  nut  d 


TURNING   ENGINES   AND    REVERSING   ENGINES  179 

were  a  fixed  point  the  valve  would  be  closed  by  the  movement 
of  the  spindle  through  the  nut  e.  If  the  nut  d  is  moved  up  or 
down  so  as  to  counteract  the  movement  of  the  spindle  through 
the  nut,  the  valve  will  be  held  open.  When  the  gear  is  to  be 
stopped  the  nut  d  is  held  fixed  and  a  slight  movement  of  the 
crosshead  turns  the  spindle  enough  to  close  the  valve. 


INDEX 


Air  leakage  into  condensers,  153. 

Air  pump,  attached,  156. 

Air  pump  capacity,  155. 

Air  pump  and  condenser,  relation  of, 

149. 
Air  pump  proportions,  157. 
Air  pumps,  two-stage,  138. 
Air  pumps,  types  of,  159. 
Argonaut   H.M.S.   steam   consumption 

tests,  17. 
Augmentor  condenser,  138. 

Backing  guides,  61. 

Balance  of  single-crank  engine,  115. 

Balance  of  two-crank  engine,  115. 

Balance  of  three-crank  engine,  116. 

Balance  of  four-crank  engine,  117. 

Balance  of  engines  of  five  or  more 
cranks,  122. 

Balancing  of  engines,  102. 

Balancing  of  rotating  masses,  105. 

Bearing  pressures,  38. 

Bearing  pressures,  table  of,  40. 

Bending  moment,  maximum,  43. 

Birmingham,  U.  S.  S.  steam  consump- 
tion tests,  17. 

Bolts,  working  load  for,  36. 

Boring  bar,  opening  for,  in  cylinder,  77. 

Centrifugal  force  of  crank,  82. 
Character  of  load,  effect  of,  upon  work- 
ing stress  factor,  34. 
Clearance  volumes,  20. 
Column  formula,  37. 
Column  sizes,  curves  for,  55. 
Columns,  hollow,  38. 
Combined  bearings,  82. 
Condenser,  jet,  131. 
Condenser,  surface,  131. 
Condenser  tubes,  size  of,  149. 


Condensers,  Weighton's  experiments 
upon, 140. 

Conditions  affecting  design  factors,  6. 

Connecting-rod  bolts,  66. 

Connecting-rod  boxes,  66. 

Connecting-rod  brasses,  68. 

Connecting-rod  caps,  68. 

Connecting-rod  fork,  66. 

Connecting-rod,  diameter  of,  63. 

Connecting-rods,  taper  of  body,  65. 

Connecting-rods,  types  of,  62. 

Conversion  of  heat  into  work,  i. 

Cooling  surface,  efficiency  of,  132. 

CooHng  water,  velocity  of,  130,  145. 

Coupling  bolts,  45. 

Crank-pin  load,  83. 

Crank  shafts  for  internal  combustion 
engines,  Lloyd's  rules  for,  48. 

Crank  shafts,  Lloyd's  rules  for,  46. 

Crank-shaft  parts,  size  of,  46. 

Crank  arrangement,  effect  of,  upon 
steam  consumption,  13. 

Cut-off,  curves  for  determination  of,  24. 

Crossheads,  55. 

Crosshead,  acceleration  of,  107. 

Crosshead  block,  57. 

Crosshead  pins,  57. 

Cut-off,  effects  of,  on  economy  and 
power,  II. 

Cut-offs,  effect  of,  upon  cylinder  vol- 
ume ratios,  21. 

Cylinder  arrangements,  87. 

Cylinder  castings,  72. 

Cylinder  ends,  72. 

Cylinder  feet,  76. 

Cylinder  openings,  76. 

Cylinder  ports  and  passages,  75. 

Cylinder  column  bolts,  84. 

Cylinder  column  flanges,  84. 

Cylinder-cover  studs,  77. 


181 


Ib2 


INDEX 


Cylinder  ratio,  relation  of,  to  cut-off,  12. 

Cylinder  supports,  83. 

Cylinder,  thickness  of  parts  of,  72. 

Delaware,  U.  S.  S.,  steam  consumption 

tests,  17. 
Design,  example  of,  23. 
Design  factors,  2. 
Design  of  surface  condensers,  142. 
Drag  rods,  97. 

Eccentric  rods,  97. 

Eccentric  strap,  99. 

Engine  beds,  85. 

Engines,  space  occupied  by,  88. 

Equivalent  twisting  or  bending  mo- 
ments, 41. 

Expansions,  determination  of  number 
of,  19. 

Flat  slide  valve,  size  of,  91. 
Force  and  moment  diagrams,  112. 

Heat  transmission,  rate  of,  1 29. 

H.P.  cylinder,  determination  of  size  of, 

20. 
High  vacua,  means  employed  to  obtain, 

136. 

Inertia,  effect  of,  upon  maximum  twist- 
ing moment,  42. 

Intermediate  cylinders,  determination 
of  size,  21. 

Jacketing,  10. 

Liner,  attachment  of,  to  cylinder,  74. 
Link  bars,  97. 
Link-block  pin,  98. 
Load  upon  crank  pms,  83. 
Load  upon  main  bearings,  80. 
Load  upon  turning  engine,  167. 
Load  upon  valve  gear,  94,  100. 
L.P.  Cylinder,  determination  of  size  of, 
19. 

Main  bearing  bolts,  86. 
Main  bearing  caps,  87. 


Main  bearing,  character  of  load  upon; 

78. 
Main  bearing  loads,  80. 
McBride's  diagram,  150,  151. 
Mean  effective  pressure,  best  values  of, 

16. 
Mean  effective  pressure,  effect  of,  upon 

steam  consumption,  14. 
Mean  referred  pressure,  i. 
Mean   referred  pressure,   variation  of, 

at  reduced  power,  33. 
Measurement  of  power,  i. 

Neilson's  diagram,  150,  151. 

Partial  pressures,  125. 
Piston,  cast  iron,  69. 
Piston,  cast  steel,  70, 
Piston  rims,  72. 
Piston  rings,  71. 
Piston  rod,  diameter  of,  53. 
Piston  rod,  ends  of,  54. 
Piston  rod  loads,  53. 
Piston  valves,  size  of,  90. 
Power  distribution  among  cylinders,  23. 
Pressure    allowed    upon    bearing    sur- 
faces, 40. 
Primary  and  secondary  masses,  109. 

Rate  of  condensation,  effect  of  air  upon, 
125. 

Rate  of  vibration  of  shafting,  52. 

Receiver  drop  in  multiple-expansion  en- 
gines, II. 

Reduced  power,  distribution  of  work 
at,  30. 

Reheating,  9. 

Rev^erse  shaft,  100. 

Reverse  shaft  levers,  100. 

Reversing  engines,  173. 

Revolutions,  variation  of,  at  reduced 
power,  2,2>- 

Shaft  diameter,  determination  of,  from 
equivalent  bending  moment,  44. 

Shaft  diameter,  determination  of,  from 
equivalent  twisting  moment,  43. 

Shafting,  types  of,  40. 


INDEX 


183 


Slippers  for  crossheads,  attachment  of, 

62. 
Slippers  for  crossheads,  size  of,  60. 
Slippers  for  crossheads,  types  of,  58. 
Steam  consumption,  28. 
Steam  consmnption  tests,  16. 
Steam  speeds,  89. 
Stroke,  usual  values  for,  22. 
Superheat  factor,  effect  of,  upon  design, 

22. 
Superheated  steam,  7. 
Superheated  steam  factor,  8. 
Surface-section  ratio,  147. 

Texas,   U.   S.   S.,   steam  consumption 

tests,  17. 
Threaded  parts,  working  stress  for,  36. 
Torsional  vibration  of  shafting,  49. 
Tube  length,  129. 
Turning  engines,  167. 
Twisting  moments,  maximum,  42. 


Twisting  moments,  mean,  41. 

Vacuum,    effect   of,   upon   steam   con- 
sumption, 13. 
Valve-chest  cover  and  studs,  78. 
Valve  diagram,  89. 
Valve  gear,  94. 
Valve  gear  balance,  no. 
Valve  stem,  load  upon,  94,  100. 
Valve-stem  yokes,  97. 

Working  load  for  bolts,  36. 

Working  stress  factor,  34. 

Working  stress  factor,  effect  of  charac- 
ter of  load  upon,  34. 

Worm  and  wheel,  design  of,  169. 

Worm  and  wheel,  proportions  of  teeth 
of,  169. 

Yarrow-Schlick-Tweedy  system  of  bal- 
ance, 117. 


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